8/19/2019 y = ln (kx) / ln (k)

1/443

 A^n = 2A

then n=ln2A / lnA

 A 2A lnA ln2A

0 0 Err:502 Err:502

0.1 0.2 -2.302585093 -1.6094379124

0.2 0.4 -1.6094379124 -0.9162907319

0.3 0.6 -1.2039728043 -0.5108256238

0.4 0.8 -0.9162907319 -0.2231435513

0.5 1 -0.6931471806 0

0.6 1.2 -0.5108256238 0.1823215568

0.7 1.4 -0.3566749439 0.3364722366

0.8 1.6 -0.2231435513 0.4700036292

0.9 1.8 -0.1053605157 0.5877866649

1 2 0 0.69314718061.1 2.2 0.0953101798 0.7884573604

1.2 2.4 0.1823215568 0.8754687374

1.3 2.6 0.2623642645 0.955511445

1.4 2.8 0.3364722366 1.0296194172

1.5 3 0.4054651081 1.0986122887

1.6 3.2 0.4700036292 1.1631508098

1.7 3.4 0.5306282511 1.2237754316

1.8 3.6 0.5877866649 1.2809338455

1.9 3.8 0.6418538862 1.3350010667

2 4 0.6931471806 1.3862943611

2.1 4.2 0.7419373447 1.4350845253

2.2 4.4 0.7884573604 1.4816045409

2.3 4.6 0.8329091229 1.5260563035

2.4 4.8 0.8754687374 1.5686159179

2.5 5 0.9162907319 1.6094379124

2.6 5.2 0.955511445 1.6486586256

2.7 5.4 0.993251773 1.68639895362.8 5.6 1.0296194172 1.7227665977

2.9 5.8 1.064710737 1.7578579176

3 6 1.0986122887 1.7917594692

3.1 6.2 1.1314021115 1.8245492921

3.2 6.4 1.1631508098 1.8562979904

3.3 6.6 1.1939224685 1.887069649

3.4 6.8 1.2237754316 1.9169226122

8/19/2019 y = ln (kx) / ln (k)

2/443

3.5 7 1.2527629685 1.9459101491

3.6 7.2 1.2809338455 1.974081026

3.7 7.4 1.3083328197 2.0014800002

3.8 7.6 1.3350010667 2.0281482473

3.9 7.8 1.3609765531 2.0541237337

4 8 1.3862943611 2.0794415417

4.1 8.2 1.4109869737 2.1041341543

4.2 8.4 1.4350845253 2.1282317058

4.3 8.6 1.4586150227 2.1517622033

4.4 8.8 1.4816045409 2.1747517215

4.5 9 1.5040773968 2.1972245773

4.6 9.2 1.5260563035 2.2192034841

4.7 9.4 1.5475625087 2.2407096893

4.8 9.6 1.5686159179 2.2617630985

4.9 9.8 1.5892352051 2.2823823857

5 10 1.6094379124 2.302585093

5.1 10.2 1.6292405397 2.3223877203

5.2 10.4 1.6486586256 2.3418058061

5.3 10.6 1.6677068206 2.3608540011

5.4 10.8 1.6863989536 2.3795461341

5.5 11 1.7047480922 2.3978952728

5.6 11.2 1.7227665977 2.4159137783

5.7 11.4 1.7404661748 2.4336133554

5.8 11.6 1.7578579176 2.4510050981

5.9 11.8 1.7749523509 2.4680995315

6 12 1.7917594692 2.4849066498

6.1 12.2 1.8082887712 2.5014359517

6.2 12.4 1.8245492921 2.5176964726

6.3 12.6 1.8405496334 2.533696814

6.4 12.8 1.8562979904 2.5494451709

6.5 13 1.8718021769 2.56494935756.6 13.2 1.887069649 2.5802168296

6.7 13.4 1.9021075264 2.595254707

6.8 13.6 1.9169226122 2.6100697927

6.9 13.8 1.9315214116 2.6246685922

7 14 1.9459101491 2.6390573296

7.1 14.2 1.960094784 2.6532419646

7.2 14.4 1.974081026 2.6672282066

8/19/2019 y = ln (kx) / ln (k)

3/443

7.3 14.6 1.9878743482 2.6810215287

7.4 14.8 2.0014800002 2.6946271808

7.5 15 2.0149030205 2.7080502011

7.6 15.2 2.0281482473 2.7212954279

7.7 15.4 2.0412203289 2.7343675094

7.8 15.6 2.0541237337 2.7472709143

7.9 15.8 2.0668627595 2.76000994

8 16 2.0794415417 2.7725887222

8.1 16.2 2.0918640617 2.7850112422

8.2 16.4 2.1041341543 2.7972813348

8.3 16.6 2.1162555148 2.8094026954

8.4 16.8 2.1282317058 2.8213788864

8.5 17 2.1400661635 2.8332133441

8.6 17.2 2.1517622033 2.8449093838

8.7 17.4 2.1633230257 2.8564702062

8.8 17.6 2.1747517215 2.867898902

8.9 17.8 2.1860512767 2.8791984573

9 18 2.1972245773 2.8903717579

9.1 18.2 2.2082744135 2.9014215941

9.2 18.4 2.2192034841 2.9123506646

9.3 18.6 2.2300144002 2.9231615807

9.4 18.8 2.2407096893 2.9338568698

9.5 19 2.2512917986 2.9444389792

9.6 19.2 2.2617630985 2.954910279

9.7 19.4 2.2721258855 2.9652730661

9.8 19.6 2.2823823857 2.9755295662

9.9 19.8 2.2925347571 2.9856819377

10 20 2.302585093 2.9957322736

8/19/2019 y = ln (kx) / ln (k)

4/443

n A^n (=2A)

0   1

0.6989700043 0.2

0.5693234419 0.4

0.4242833575 0.6

0.2435292026 0.8

0 1

-0.3569154489 1.2

-0.9433582099 1.4

-2.1062837195 1.6

-5.578813479 1.8

#DIV/0 #DIV/0

8.2725408973 2.2

4.8017840169 2.4

3.6419267958 2.6

3.0600427171 2.8

2.7095112914 3

2.4747698474 3.2

2.3062764359 3.4

2.1792495848 3.6

2.079914285 3.8

2 4

1.9342395089 4.2

1.8791181558 4.4

1.8322002503 4.6

1.7917440692 4.8

1.7564707974 5

1.7254200713 5.2

1.6978564745 5.41.6732071764 5.6

1.6510192454 5.8

1.6309297536 6

1.6126444113 6.2

1.5959220204 6.4

1.5805629753 6.6

1.5664006342 6.8

0 2

-8

-6

-4

-2

0

2

4

6

8

10

8/19/2019 y = ln (kx) / ln (k)

5/443

1.5532947557 7

1.5411264469 7.2

1.5297942314 7.4

1.5192109563 7.6

1.5093013388 7.8

1.5 8

1.4912498793 8.2

1.4830009441 8.4

1.4752091332 8.6

1.4678354861 8.8

1.4608454206 9

1.4542081304 9.2

1.4478960796 9.4

1.4418845765 9.6

1.4361514132 9.8

1.4306765581 10

1.4254418937 10.2

1.4204309915 10.4

1.4156289175 10.6

1.4110220651 10.8

1.4065980092 11

1.4023453795 11.2

1.3982537498 11.4

1.3943135413 11.6

1.3905159371 11.8

1.3868528072 12

1.3833166426 12.2

1.3799004957 12.4

1.3765979292 12.6

1.3734029688 12.8

1.3703100622 131.3673140421 13.2

1.364410093 13.4

1.3615937212 13.6

1.3588607283 13.8

1.3562071871 14

1.3536294195 14.2

1.3511239769 14.4

8/19/2019 y = ln (kx) / ln (k)

6/443

1.3486876226 14.6

1.3463173154 14.8

1.3440101948 15

1.3417635676 15.2

1.3395748958 15.4

1.3374417856 15.6

1.3353619767 15.8

1.3333333333 16

1.3313538357 16.2

1.3294215719 16.4

1.3275347309 16.6

1.3256915958 16.8

1.3238905378 17

1.3221300102 17.2

1.3204085439 17.4

1.3187247416 17.6

1.3170772744 17.8

1.3154648768 18

1.3138863433 18.2

1.3123405247 18.4

1.3108263249 18.6

1.3093426979 18.8

1.3078886446 19

1.3064632105 19.2

1.3050654829 19.4

1.303694589 19.6

1.3023496932 19.8

1.3010299957 20

8/19/2019 y = ln (kx) / ln (k)

7/443

4 6

n vs. A

8/19/2019 y = ln (kx) / ln (k)

8/443

8/19/2019 y = ln (kx) / ln (k)

9/443

8/19/2019 y = ln (kx) / ln (k)

10/443

8 10

n

8/19/2019 y = ln (kx) / ln (k)

11/443

8/19/2019 y = ln (kx) / ln (k)

12/443

8/19/2019 y = ln (kx) / ln (k)

13/443

 A^n = 2A

then n=ln2A / lnA

  2A lnA ln2A

0 0 Err:502 Err:502

0.1 0.2 -2.302585093 -1.6094379124

0.2 0.4 -1.6094379124 -0.9162907319

0.3 0.6 -1.2039728043 -0.5108256238

0.4 0.8 -0.9162907319 -0.2231435513

0.5 1 -0.6931471806 0

0.6 1.2 -0.5108256238 0.1823215568

0.7 1.4 -0.3566749439 0.3364722366

0.8 1.6 -0.2231435513 0.4700036292

0.9 1.8 -0.1053605157 0.5877866649

1 2 0 0.6931471806

1.1 2.2 0.0953101798 0.7884573604

1.2 2.4 0.1823215568 0.8754687374

1.3 2.6 0.2623642645 0.955511445

1.4 2.8 0.3364722366 1.0296194172

1.5 3 0.4054651081 1.0986122887

1.6 3.2 0.4700036292 1.1631508098

1.7 3.4 0.5306282511 1.2237754316

1.8 3.6 0.5877866649 1.2809338455

1.9 3.8 0.6418538862 1.3350010667

2 4 0.6931471806 1.3862943611

2.1 4.2 0.7419373447 1.4350845253

2.2 4.4 0.7884573604 1.4816045409

2.3 4.6 0.8329091229 1.5260563035

2.4 4.8 0.8754687374 1.5686159179

2.5 5 0.9162907319 1.6094379124

2.6 5.2 0.955511445 1.6486586256

2.7 5.4 0.993251773 1.68639895362.8 5.6 1.0296194172 1.7227665977

2.9 5.8 1.064710737 1.7578579176

3 6 1.0986122887 1.7917594692

3.1 6.2 1.1314021115 1.8245492921

3.2 6.4 1.1631508098 1.8562979904

3.3 6.6 1.1939224685 1.887069649

3.4 6.8 1.2237754316 1.9169226122

8/19/2019 y = ln (kx) / ln (k)

14/443

3.5 7 1.2527629685 1.9459101491

3.6 7.2 1.2809338455 1.974081026

3.7 7.4 1.3083328197 2.0014800002

3.8 7.6 1.3350010667 2.0281482473

3.9 7.8 1.3609765531 2.0541237337

4 8 1.3862943611 2.0794415417

4.1 8.2 1.4109869737 2.1041341543

4.2 8.4 1.4350845253 2.1282317058

4.3 8.6 1.4586150227 2.1517622033

4.4 8.8 1.4816045409 2.1747517215

4.5 9 1.5040773968 2.1972245773

4.6 9.2 1.5260563035 2.2192034841

4.7 9.4 1.5475625087 2.2407096893

4.8 9.6 1.5686159179 2.2617630985

4.9 9.8 1.5892352051 2.2823823857

5 10 1.6094379124 2.302585093

5.1 10.2 1.6292405397 2.3223877203

5.2 10.4 1.6486586256 2.3418058061

5.3 10.6 1.6677068206 2.3608540011

5.4 10.8 1.6863989536 2.3795461341

5.5 11 1.7047480922 2.3978952728

5.6 11.2 1.7227665977 2.4159137783

5.7 11.4 1.7404661748 2.4336133554

5.8 11.6 1.7578579176 2.4510050981

5.9 11.8 1.7749523509 2.4680995315

6 12 1.7917594692 2.4849066498

6.1 12.2 1.8082887712 2.5014359517

6.2 12.4 1.8245492921 2.5176964726

6.3 12.6 1.8405496334 2.533696814

6.4 12.8 1.8562979904 2.5494451709

6.5 13 1.8718021769 2.56494935756.6 13.2 1.887069649 2.5802168296

6.7 13.4 1.9021075264 2.595254707

6.8 13.6 1.9169226122 2.6100697927

6.9 13.8 1.9315214116 2.6246685922

7 14 1.9459101491 2.6390573296

7.1 14.2 1.960094784 2.6532419646

7.2 14.4 1.974081026 2.6672282066

8/19/2019 y = ln (kx) / ln (k)

15/443

7.3 14.6 1.9878743482 2.6810215287

7.4 14.8 2.0014800002 2.6946271808

7.5 15 2.0149030205 2.7080502011

7.6 15.2 2.0281482473 2.7212954279

7.7 15.4 2.0412203289 2.7343675094

7.8 15.6 2.0541237337 2.7472709143

7.9 15.8 2.0668627595 2.76000994

8 16 2.0794415417 2.7725887222

8.1 16.2 2.0918640617 2.7850112422

8.2 16.4 2.1041341543 2.7972813348

8.3 16.6 2.1162555148 2.8094026954

8.4 16.8 2.1282317058 2.8213788864

8.5 17 2.1400661635 2.8332133441

8.6 17.2 2.1517622033 2.8449093838

8.7 17.4 2.1633230257 2.8564702062

8.8 17.6 2.1747517215 2.867898902

8.9 17.8 2.1860512767 2.8791984573

9 18 2.1972245773 2.8903717579

9.1 18.2 2.2082744135 2.9014215941

9.2 18.4 2.2192034841 2.9123506646

9.3 18.6 2.2300144002 2.9231615807

9.4 18.8 2.2407096893 2.9338568698

9.5 19 2.2512917986 2.9444389792

9.6 19.2 2.2617630985 2.954910279

9.7 19.4 2.2721258855 2.9652730661

9.8 19.6 2.2823823857 2.9755295662

9.9 19.8 2.2925347571 2.9856819377

10 20 2.302585093 2.9957322736

10.1 20.2 2.3125354238 3.0056826044

10.2 20.4 2.3223877203 3.0155349009

10.3 20.6 2.3321438952 3.025291075810.4 20.8 2.3418058061 3.0349529867

10.5 21 2.3513752572 3.0445224377

10.6 21.2 2.3608540011 3.0540011817

10.7 21.4 2.3702437415 3.063390922

10.8 21.6 2.3795461341 3.0726933147

10.9 21.8 2.3887627892 3.0819099698

11 22 2.3978952728 3.0910424534

8/19/2019 y = ln (kx) / ln (k)

16/443

11.1 22.2 2.4069451083 3.1000922889

11.2 22.4 2.4159137783 3.1090609589

11.3 22.6 2.4248027257 3.1179499063

11.4 22.8 2.4336133554 3.126760536

11.5 23 2.4423470354 3.1354942159

11.6 23.2 2.4510050981 3.1441522787

11.7 23.4 2.4595888418 3.1527360224

11.8 23.6 2.4680995315 3.161246712

11.9 23.8 2.4765384001 3.1696855807

12 24 2.4849066498 3.1780538303

12.1 24.2 2.4932054526 3.1863526332

12.2 24.4 2.5014359517 3.1945831323

12.3 24.6 2.5095992624 3.2027464429

12.4 24.8 2.5176964726 3.2108436532

12.5 25 2.5257286443 3.2188758249

12.6 25.2 2.533696814 3.2268439945

12.7 25.4 2.5416019935 3.234749174

12.8 25.6 2.5494451709 3.2425923515

12.9 25.8 2.5572273114 3.2503744919

13 26 2.5649493575 3.258096538

13.1 26.2 2.5726122302 3.2657594108

13.2 26.4 2.5802168296 3.2733640102

13.3 26.6 2.5877640352 3.2809112158

13.4 26.8 2.595254707 3.2884018875

13.5 27 2.6026896854 3.295836866

13.6 27.2 2.6100697927 3.3032169733

13.7 27.4 2.6173958328 3.3105430134

13.8 27.6 2.6246685922 3.3178157727

13.9 27.8 2.6318888401 3.3250360207

14 28 2.6390573296 3.3322045102

14.1 28.2 2.6461747974 3.339321977914.2 28.4 2.6532419646 3.3463891452

14.3 28.6 2.6602595373 3.3534067178

14.4 28.8 2.6672282066 3.3603753871

14.5 29 2.6741486494 3.36729583

14.6 29.2 2.6810215287 3.3741687093

14.7 29.4 2.6878474938 3.3809946743

14.8 29.6 2.6946271808 3.3877743613

8/19/2019 y = ln (kx) / ln (k)

17/443

14.9 29.8 2.701361213 3.3945083935

15 30 2.7080502011 3.4011973817

15.1 30.2 2.7146947438 3.4078419244

15.2 30.4 2.7212954279 3.4144426084

15.3 30.6 2.7278528284 3.421000009

15.4 30.8 2.7343675094 3.42751469

15.5 31 2.7408400239 3.4339872045

15.6 31.2 2.7472709143 3.4404180948

15.7 31.4 2.7536607124 3.4468078929

15.8 31.6 2.76000994 3.4531571206

15.9 31.8 2.7663191092 3.4594662898

16 32 2.7725887222 3.4657359028

16.1 32.2 2.778819272 3.4719664526

16.2 32.4 2.7850112422 3.4781584228

16.3 32.6 2.7911651078 3.4843122884

16.4 32.8 2.7972813348 3.4904285154

16.5 33 2.8033603809 3.4965075615

16.6 33.2 2.8094026954 3.5025498759

16.7 33.4 2.8154087194 3.5085559

16.8 33.6 2.8213788864 3.514526067

16.9 33.8 2.8273136219 3.5204608025

17 34 2.8332133441 3.5263605246

17.1 34.2 2.8390784635 3.5322256441

17.2 34.4 2.8449093838 3.5380565644

17.3 34.6 2.8507065015 3.5438536821

17.4 34.8 2.8564702062 3.5496173868

17.5 35 2.8622008809 3.5553480615

17.6 35.2 2.867898902 3.5610460826

17.7 35.4 2.8735646396 3.5667118201

17.8 35.6 2.8791984573 3.5723456379

17.9 35.8 2.8848007128 3.577947893418 36 2.8903717579 3.5835189385

18.1 36.2 2.8959119383 3.5890591188

18.2 36.4 2.9014215941 3.5945687746

18.3 36.6 2.9069010598 3.6000482404

18.4 36.8 2.9123506646 3.6054978452

18.5 37 2.9177707321 3.6109179126

18.6 37.2 2.9231615807 3.6163087613

8/19/2019 y = ln (kx) / ln (k)

18/443

18.7 37.4 2.9285235239 3.6216707044

18.8 37.6 2.9338568698 3.6270040504

18.9 37.8 2.9391619221 3.6323091026

19 38 2.9444389792 3.6375861597

19.1 38.2 2.9496883351 3.6428355156

19.2 38.4 2.954910279 3.6480574596

19.3 38.6 2.9601050959 3.6532522765

19.4 38.8 2.9652730661 3.6584202466

19.5 39 2.9704144656 3.6635616461

19.6 39.2 2.9755295662 3.6686767468

19.7 39.4 2.9806186357 3.6737658163

19.8 39.6 2.9856819377 3.6788291183

19.9 39.8 2.9907197317 3.6838669123

20 40 2.9957322736 3.6888794541

20.1 40.2 3.0007198151 3.6938669956

20.2 40.4 3.0056826044 3.698829785

20.3 40.6 3.010620886 3.7037680666

20.4 40.8 3.0155349009 3.7086820814

20.5 41 3.0204248861 3.7135720667

20.6 41.2 3.0252910758 3.7184382564

20.7 41.4 3.0301337003 3.7232808808

20.8 41.6 3.0349529867 3.7281001673

20.9 41.8 3.039749159 3.7328963395

21 42 3.0445224377 3.7376696183

21.1 42.2 3.0492730405 3.742420221

21.2 42.4 3.0540011817 3.7471483622

21.3 42.6 3.0587070727 3.7518542533

21.4 42.8 3.063390922 3.7565381026

21.5 43 3.0680529351 3.7612001157

21.6 43.2 3.0726933147 3.7658404953

21.7 43.4 3.0773122605 3.770459441121.8 43.6 3.0819099698 3.7750571504

21.9 43.8 3.0864866368 3.7796338174

22 44 3.0910424534 3.7841896339

22.1 44.2 3.0955776085 3.7887247891

22.2 44.4 3.1000922889 3.7932394694

22.3 44.6 3.1045866785 3.797733859

22.4 44.8 3.1090609589 3.8022081394

8/19/2019 y = ln (kx) / ln (k)

19/443

22.5 45 3.1135153092 3.8066624898

22.6 45.2 3.1179499063 3.8110970868

22.7 45.4 3.1223649245 3.815512105

22.8 45.6 3.126760536 3.8199077165

22.9 45.8 3.1311369106 3.8242840911

23 46 3.1354942159 3.8286413965

23.1 46.2 3.1398326175 3.8329797981

23.2 46.4 3.1441522787 3.8372994592

23.3 46.6 3.1484533606 3.8416005411

23.4 46.8 3.1527360224 3.8458832029

23.5 47 3.1570004212 3.8501476017

23.6 47.2 3.161246712 3.8543938926

23.7 47.4 3.1654750481 3.8586222287

23.8 47.6 3.1696855807 3.8628327612

23.9 47.8 3.1738784589 3.8670256395

24 48 3.1780538303 3.8712010109

24.1 48.2 3.1822118405 3.8753590211

24.2 48.4 3.1863526332 3.8794998137

24.3 48.6 3.1904763503 3.8836235309

24.4 48.8 3.1945831323 3.8877303129

24.5 49 3.1986731176 3.8918202981

24.6 49.2 3.2027464429 3.8958936235

24.7 49.4 3.2068032436 3.8999504242

24.8 49.6 3.2108436532 3.9039908337

24.9 49.8 3.2148678035 3.908014984

25 50 3.2188758249 3.9120230054

25.1 50.2 3.2228678461 3.9160150267

25.2 50.4 3.2268439945 3.9199911751

25.3 50.6 3.2308043957 3.9239515763

25.4 50.8 3.234749174 3.9278963546

25.5 51 3.2386784522 3.931825632725.6 51.2 3.2425923515 3.935739532

25.7 51.4 3.2464909919 3.9396381725

25.8 51.6 3.2503744919 3.9435216725

25.9 51.8 3.2542429687 3.9473901493

26 52 3.258096538 3.9512437186

26.1 52.2 3.2619353143 3.9550824949

26.2 52.4 3.2657594108 3.9589065913

8/19/2019 y = ln (kx) / ln (k)

20/443

26.3 52.6 3.2695689392 3.9627161197

26.4 52.8 3.2733640102 3.9665111907

26.5 53 3.277144733 3.9702919136

26.6 53.2 3.2809112158 3.9740583963

26.7 53.4 3.2846635654 3.977810746

26.8 53.6 3.2884018875 3.9815490681

26.9 53.8 3.2921262866 3.9852734672

27 54 3.295836866 3.9889840466

27.1 54.2 3.2995337279 3.9926809084

27.2 54.4 3.3032169733 3.9963641539

27.3 54.6 3.3068867022 4.0000338828

27.4 54.8 3.3105430134 4.003690194

27.5 55 3.3141860047 4.0073331852

27.6 55.2 3.3178157727 4.0109629533

27.7 55.4 3.3214324132 4.0145795938

27.8 55.6 3.3250360207 4.0181832013

27.9 55.8 3.3286266888 4.0217738694

28 56 3.3322045102 4.0253516907

28.1 56.2 3.3357695763 4.0289167569

28.2 56.4 3.3393219779 4.0324691585

28.3 56.6 3.3428618046 4.0360089852

28.4 56.8 3.3463891452 4.0395363257

28.5 57 3.3499040873 4.0430512678

28.6 57.2 3.3534067178 4.0465538984

28.7 57.4 3.3568971228 4.0500443033

28.8 57.6 3.3603753871 4.0535225677

28.9 57.8 3.3638415951 4.0569887757

29 58 3.36729583 4.0604430105

29.1 58.2 3.3707381742 4.0638853547

29.2 58.4 3.3741687093 4.0673158898

29.3 58.6 3.377587516 4.070734696629.4 58.8 3.3809946743 4.0741418549

29.5 59 3.3843902633 4.0775374439

29.6 59.2 3.3877743613 4.0809215419

29.7 59.4 3.3911470458 4.0842942264

29.8 59.6 3.3945083935 4.0876555741

29.9 59.8 3.3978584804 4.091005661

30 60 3.4011973817 4.0943445622

8/19/2019 y = ln (kx) / ln (k)

21/443

30.1 60.2 3.4045251718 4.0976723523

30.2 60.4 3.4078419244 4.1009891049

30.3 60.6 3.4111477125 4.1042948931

30.4 60.8 3.4144426084 4.107589789

30.5 61 3.4177266836 4.1108738642

30.6 61.2 3.421000009 4.1141471895

30.7 61.4 3.4242626546 4.1174098352

30.8 61.6 3.42751469 4.1206618705

30.9 61.8 3.4307561839 4.1239033645

31 62 3.4339872045 4.127134385

31.1 62.2 3.4372078192 4.1303549997

31.2 62.4 3.4404180948 4.1335652754

31.3 62.6 3.4436180975 4.1367652781

31.4 62.8 3.4468078929 4.1399550735

31.5 63 3.4499875458 4.1431347264

31.6 63.2 3.4531571206 4.1463043012

31.7 63.4 3.4563166809 4.1494638614

31.8 63.6 3.4594662898 4.1526134703

31.9 63.8 3.4626060098 4.1557531904

32 64 3.4657359028 4.1588830834

32.1 64.2 3.4688560301 4.1620032107

32.2 64.4 3.4719664526 4.1651136331

32.3 64.6 3.4750672302 4.1682144108

32.4 64.8 3.4781584228 4.1713056034

32.5 65 3.4812400893 4.1743872699

32.6 65.2 3.4843122884 4.1774594689

32.7 65.4 3.4873750779 4.1805222585

32.8 65.6 3.4904285154 4.183575696

32.9 65.8 3.4934726578 4.1866198383

33 66 3.4965075615 4.189654742

33.1 66.2 3.4995332824 4.192680462933.2 66.4 3.5025498759 4.1956970565

33.3 66.6 3.505557397 4.1987045775

33.4 66.8 3.5085559 4.2017030805

33.5 67 3.5115454388 4.2046926194

33.6 67.2 3.514526067 4.2076732475

33.7 67.4 3.5174978374 4.2106450179

33.8 67.6 3.5204608025 4.213607983

8/19/2019 y = ln (kx) / ln (k)

22/443

33.9 67.8 3.5234150144 4.2165621949

34 68 3.5263605246 4.2195077052

34.1 68.2 3.5292973843 4.2224445648

34.2 68.4 3.5322256441 4.2253728246

34.3 68.6 3.5351453542 4.2282925347

34.4 68.8 3.5380565644 4.2312037449

34.5 69 3.540959324 4.2341065046

34.6 69.2 3.5438536821 4.2370008626

34.7 69.4 3.546739687 4.2398868675

34.8 69.6 3.5496173868 4.2427645673

34.9 69.8 3.5524868292 4.2456340098

35 70 3.5553480615 4.248495242

35.1 70.2 3.5582011305 4.251348311

35.2 70.4 3.5610460826 4.2541932632

35.3 70.6 3.5638829639 4.2570301445

35.4 70.8 3.5667118201 4.2598590007

35.5 71 3.5695326965 4.262679877

35.6 71.2 3.5723456379 4.2654928184

35.7 71.4 3.5751506888 4.2682978693

35.8 71.6 3.5779478934 4.271095074

35.9 71.8 3.5807372955 4.2738844761

36 72 3.5835189385 4.276666119

36.1 72.2 3.5862928653 4.2794400459

36.2 72.4 3.5890591188 4.2822062994

36.3 72.6 3.5918177413 4.2849649218

36.4 72.8 3.5945687746 4.2877159552

36.5 73 3.5973122606 4.2904594411

36.6 73.2 3.6000482404 4.293195421

36.7 73.4 3.6027767551 4.2959239356

36.8 73.6 3.6054978452 4.2986450257

36.9 73.8 3.608211551 4.301358731637 74 3.6109179126 4.3040650932

37.1 74.2 3.6136169696 4.3067641502

37.2 74.4 3.6163087613 4.3094559418

37.3 74.6 3.6189933266 4.3121405072

37.4 74.8 3.6216707044 4.314817885

37.5 75 3.624340933 4.3174881135

37.6 75.2 3.6270040504 4.320151231

8/19/2019 y = ln (kx) / ln (k)

23/443

37.7 75.4 3.6296600945 4.322807275

37.8 75.6 3.6323091026 4.3254562832

37.9 75.8 3.6349511121 4.3280982926

38 76 3.6375861597 4.3307333403

38.1 76.2 3.6402142821 4.3333614627

38.2 76.4 3.6428355156 4.3359826962

38.3 76.6 3.6454498962 4.3385970767

38.4 76.8 3.6480574596 4.3412046402

38.5 77 3.6506582413 4.3438054219

38.6 77.2 3.6532522765 4.346399457

38.7 77.4 3.6558396 4.3489867806

38.8 77.6 3.6584202466 4.3515674272

38.9 77.8 3.6609942506 4.3541414312

39 78 3.6635616461 4.3567088267

39.1 78.2 3.666122467 4.3592696476

39.2 78.4 3.6686767468 4.3618239274

39.3 78.6 3.6712245189 4.3643716994

39.4 78.8 3.6737658163 4.3669129969

39.5 79 3.6763006719 4.3694478525

39.6 79.2 3.6788291183 4.3719762988

39.7 79.4 3.6813511877 4.3744983683

39.8 79.6 3.6838669123 4.3770140929

39.9 79.8 3.6863763239 4.3795235045

40 80 3.6888794541 4.3820266347

40.1 80.2 3.6913763343 4.3845235149

40.2 80.4 3.6938669956 4.3870141762

40.3 80.6 3.696351469 4.3894986495

40.4 80.8 3.698829785 4.3919769655

40.5 81 3.7013019741 4.3944491547

40.6 81.2 3.7037680666 4.3969152472

40.7 81.4 3.7062280924 4.39937527340.8 81.6 3.7086820814 4.401829262

40.9 81.8 3.711130063 4.4042772436

41 82 3.7135720667 4.4067192473

41.1 82.2 3.7160081215 4.4091553021

41.2 82.4 3.7184382564 4.4115854369

41.3 82.6 3.7208625 4.4140096805

41.4 82.8 3.7232808808 4.4164280614

8/19/2019 y = ln (kx) / ln (k)

24/443

41.5 83 3.7256934272 4.4188406078

41.6 83.2 3.7281001673 4.4212473478

41.7 83.4 3.7305011288 4.4236483094

41.8 83.6 3.7328963395 4.4260435201

41.9 83.8 3.7352858269 4.4284330075

42 84 3.7376696183 4.4308167988

42.1 84.2 3.7400477407 4.4331949212

42.2 84.4 3.742420221 4.4355674016

42.3 84.6 3.7447870861 4.4379342666

42.4 84.8 3.7471483622 4.4402955428

42.5 85 3.7495040759 4.4426512565

42.6 85.2 3.7518542533 4.4450014338

42.7 85.4 3.7541989202 4.4473461008

42.8 85.6 3.7565381026 4.4496852831

42.9 85.8 3.7588718259 4.4520190065

43 86 3.7612001157 4.4543472963

43.1 86.2 3.7635229971 4.4566701777

43.2 86.4 3.7658404953 4.4589876758

43.3 86.6 3.768152635 4.4612998156

43.4 86.8 3.7704594411 4.4636066217

43.5 87 3.7727609381 4.4659081187

43.6 87.2 3.7750571504 4.4682043309

43.7 87.4 3.7773481021 4.4704952827

43.8 87.6 3.7796338174 4.4727809979

43.9 87.8 3.7819143201 4.4750615006

44 88 3.7841896339 4.4773368145

44.1 88.2 3.7864597825 4.479606963

44.2 88.4 3.7887247891 4.4818719696

44.3 88.6 3.7909846771 4.4841318576

44.4 88.8 3.7932394694 4.48638665

44.5 89 3.7954891892 4.488636369744.6 89.2 3.797733859 4.4908810396

44.7 89.4 3.7999735016 4.4931206822

44.8 89.6 3.8022081394 4.49535532

44.9 89.8 3.8044377947 4.4975849753

45 90 3.8066624898 4.4998096703

45.1 90.2 3.8088822465 4.5020294271

45.2 90.4 3.8110970868 4.5042442674

8/19/2019 y = ln (kx) / ln (k)

25/443

45.3 90.6 3.8133070325 4.506454213

45.4 90.8 3.815512105 4.5086592856

45.5 91 3.817712326 4.5108595065

45.6 91.2 3.8199077165 4.5130548971

45.7 91.4 3.8220982979 4.5152454785

45.8 91.6 3.8242840911 4.5174312717

45.9 91.8 3.8264651171 4.5196122976

46 92 3.8286413965 4.521788577

46.1 92.2 3.83081295 4.5239601306

46.2 92.4 3.8329797981 4.5261269786

46.3 92.6 3.8351419611 4.5282891417

46.4 92.8 3.8372994592 4.5304466398

46.5 93 3.8394523126 4.5325994932

46.6 93.2 3.8416005411 4.5347477217

46.7 93.4 3.8437441647 4.5368913452

46.8 93.6 3.8458832029 4.5390303835

46.9 93.8 3.8480176755 4.541164856

47 94 3.8501476017 4.5432947823

47.1 94.2 3.852273001 4.5454201816

47.2 94.4 3.8543938926 4.5475410732

47.3 94.6 3.8565102955 4.5496574761

47.4 94.8 3.8586222287 4.5517694093

47.5 95 3.860729711 4.5538768916

47.6 95.2 3.8628327612 4.5559799418

47.7 95.4 3.8649313979 4.5580785785

47.8 95.6 3.8670256395 4.5601728201

47.9 95.8 3.8691155044 4.562262685

48 96 3.8712010109 4.5643481915

48.1 96.2 3.8732821771 4.5664293577

48.2 96.4 3.8753590211 4.5685062016

48.3 96.6 3.8774315607 4.570578741248.4 96.8 3.8794998137 4.5726469943

48.5 97 3.8815637979 4.5747109785

48.6 97.2 3.8836235309 4.5767707115

48.7 97.4 3.8856790301 4.5788262106

48.8 97.6 3.8877303129 4.5808774934

48.9 97.8 3.8897773965 4.582924577

49 98 3.8918202981 4.5849674787

8/19/2019 y = ln (kx) / ln (k)

26/443

49.1 98.2 3.8938590348 4.5870062154

49.2 98.4 3.8958936235 4.5890408041

49.3 98.6 3.897924081 4.5910712616

49.4 98.8 3.8999504242 4.5930976048

49.5 99 3.9019726696 4.5951198501

49.6 99.2 3.9039908337 4.5971380143

49.7 99.4 3.9060049331 4.5991521137

49.8 99.6 3.908014984 4.6011621646

49.9 99.8 3.9100210028 4.6031681833

50 100 3.9120230054 4.605170186

50.1 100.2 3.9140210081 4.6071681887

50.2 100.4 3.9160150267 4.6091622073

50.3 100.6 3.9180050771 4.6111522577

50.4 100.8 3.9199911751 4.6131383556

50.5 101 3.9219733363 4.6151205168

50.6 101.2 3.9239515763 4.6170987569

50.7 101.4 3.9259259106 4.6190730912

50.8 101.6 3.9278963546 4.6210435351

50.9 101.8 3.9298629236 4.6230101041

51 102 3.9318256327 4.6249728133

51.1 102.2 3.9337844972 4.6269316778

51.2 102.4 3.935739532 4.6288867126

51.3 102.6 3.9376907522 4.6308379327

51.4 102.8 3.9396381725 4.632785353

51.5 103 3.9415818077 4.6347289882

51.6 103.2 3.9435216725 4.636668853

51.7 103.4 3.9454577815 4.6386049621

51.8 103.6 3.9473901493 4.6405373298

51.9 103.8 3.9493187902 4.6424659707

52 104 3.9512437186 4.6443908991

52.1 104.2 3.9531649488 4.646312129352.2 104.4 3.9550824949 4.6482296754

52.3 104.6 3.9569963711 4.6501435516

52.4 104.8 3.9589065913 4.6520537719

52.5 105 3.9608131696 4.6539603502

52.6 105.2 3.9627161197 4.6558633003

52.7 105.4 3.9646154555 4.6577626361

52.8 105.6 3.9665111907 4.6596583713

8/19/2019 y = ln (kx) / ln (k)

27/443

52.9 105.8 3.9684033389 4.6615505194

53 106 3.9702919136 4.6634390941

53.1 106.2 3.9721769282 4.6653241088

53.2 106.4 3.9740583963 4.6672055769

53.3 106.6 3.9759363312 4.6690835117

53.4 106.8 3.977810746 4.6709579265

53.5 107 3.9796816539 4.6728288345

53.6 107.2 3.9815490681 4.6746962486

53.7 107.4 3.9834130015 4.6765601821

53.8 107.6 3.9852734672 4.6784206477

53.9 107.8 3.9871304779 4.6802776585

54 108 3.9889840466 4.6821312271

54.1 108.2 3.9908341859 4.6839813664

54.2 108.4 3.9926809084 4.685828089

54.3 108.6 3.9945242269 4.6876714075

54.4 108.8 3.9963641539 4.6895113344

54.5 109 3.9982007017 4.6913478822

54.6 109.2 4.0000338828 4.6931810633

54.7 109.4 4.0018637094 4.69501089

54.8 109.6 4.003690194 4.6968373745

54.9 109.8 4.0055133485 4.6986605291

55 110 4.0073331852 4.7004803658

55.1 110.2 4.0091497162 4.7022968967

55.2 110.4 4.0109629533 4.7041101338

55.3 110.6 4.0127729085 4.7059200891

55.4 110.8 4.0145795938 4.7077267743

55.5 111 4.0163830208 4.7095302013

55.6 111.2 4.0181832013 4.7113303818

55.7 111.4 4.0199801469 4.7131273275

55.8 111.6 4.0217738694 4.7149210499

55.9 111.8 4.0235643802 4.716711560756 112 4.0253516907 4.7184988713

56.1 112.2 4.0271358125 4.7202829931

56.2 112.4 4.0289167569 4.7220639375

56.3 112.6 4.0306945351 4.7238417157

56.4 112.8 4.0324691585 4.7256163391

56.5 113 4.0342406382 4.7273878187

56.6 113.2 4.0360089852 4.7291561658

8/19/2019 y = ln (kx) / ln (k)

28/443

56.7 113.4 4.0377742107 4.7309213913

56.8 113.6 4.0395363257 4.7326835063

56.9 113.8 4.0412953411 4.7344425217

57 114 4.0430512678 4.7361984484

57.1 114.2 4.0448041167 4.7379512972

57.2 114.4 4.0465538984 4.7397010789

57.3 114.6 4.0483006237 4.7414478043

57.4 114.8 4.0500443033 4.7431914839

57.5 115 4.0517849478 4.7449321284

57.6 115.2 4.0535225677 4.7466697483

57.7 115.4 4.0552571735 4.7484043541

57.8 115.6 4.0569887757 4.7501359562

57.9 115.8 4.0587173846 4.7518645651

58 116 4.0604430105 4.7535901911

58.1 116.2 4.0621656639 4.7553128444

58.2 116.4 4.0638853547 4.7570325353

58.3 116.6 4.0656020934 4.7587492739

58.4 116.8 4.0673158898 4.7604630704

58.5 117 4.0690267542 4.7621739348

58.6 117.2 4.0707346966 4.7638818771

58.7 117.4 4.0724397268 4.7655869074

58.8 117.6 4.0741418549 4.7672890355

58.9 117.8 4.0758410907 4.7689882712

59 118 4.0775374439 4.7706846245

59.1 118.2 4.0792309244 4.772378105

59.2 118.4 4.0809215419 4.7740687224

59.3 118.6 4.082609306 4.7757564866

59.4 118.8 4.0842942264 4.7774414069

59.5 119 4.0859763126 4.7791234931

59.6 119.2 4.0876555741 4.7808027546

59.7 119.4 4.0893320204 4.78247920159.8 119.6 4.091005661 4.7841528415

59.9 119.8 4.0926765051 4.7858236857

60 120 4.0943445622 4.7874917428

60.1 120.2 4.0960098415 4.7891570221

60.2 120.4 4.0976723523 4.7908195329

60.3 120.6 4.0993321037 4.7924792843

60.4 120.8 4.1009891049 4.7941362855

8/19/2019 y = ln (kx) / ln (k)

29/443

60.5 121 4.102643365 4.7957905456

60.6 121.2 4.1042948931 4.7974420736

60.7 121.4 4.1059436981 4.7990908786

60.8 121.6 4.107589789 4.8007369695

60.9 121.8 4.1092331747 4.8023803553

61 122 4.1108738642 4.8040210447

61.1 122.2 4.1125118662 4.8056590467

61.2 122.4 4.1141471895 4.8072943701

61.3 122.6 4.1157798429 4.8089270235

61.4 122.8 4.1174098352 4.8105570157

61.5 123 4.1190371748 4.8121843554

61.6 123.2 4.1206618705 4.8138090511

61.7 123.4 4.1222839309 4.8154311115

61.8 123.6 4.1239033645 4.817050545

61.9 123.8 4.1255201797 4.8186673603

62 124 4.127134385 4.8202815656

62.1 124.2 4.1287459889 4.8218931695

62.2 124.4 4.1303549997 4.8235021803

62.3 124.6 4.1319614258 4.8251086064

62.4 124.8 4.1335652754 4.8267124559

62.5 125 4.1351665567 4.8283137373

62.6 125.2 4.1367652781 4.8299124587

62.7 125.4 4.1383614476 4.8315086282

62.8 125.6 4.1399550735 4.833102254

62.9 125.8 4.1415461637 4.8346933443

63 126 4.1431347264 4.836281907

63.1 126.2 4.1447207695 4.8378679501

63.2 126.4 4.1463043012 4.8394514817

63.3 126.6 4.1478853292 4.8410325097

63.4 126.8 4.1494638614 4.842611042

63.5 127 4.1510399059 4.844187086563.6 127.2 4.1526134703 4.8457606509

63.7 127.4 4.1541845626 4.8473317431

63.8 127.6 4.1557531904 4.8489003709

63.9 127.8 4.1573193614 4.8504665419

64 128 4.1588830834 4.8520302639

64.1 128.2 4.1604443639 4.8535915445

64.2 128.4 4.1620032107 4.8551503913

8/19/2019 y = ln (kx) / ln (k)

30/443

64.3 128.6 4.1635596312 4.8567068118

64.4 128.8 4.1651136331 4.8582608137

64.5 129 4.1666652238 4.8598124044

64.6 129.2 4.1682144108 4.8613615913

64.7 129.4 4.1697612015 4.8629083821

64.8 129.6 4.1713056034 4.8644527839

64.9 129.8 4.1728476237 4.8659948043

65 130 4.1743872699 4.8675344505

65.1 130.2 4.1759245492 4.8690717298

65.2 130.4 4.1774594689 4.8706066495

65.3 130.6 4.1789920363 4.8721392168

65.4 130.8 4.1805222585 4.873669439

65.5 131 4.1820501426 4.8751973232

65.6 131.2 4.183575696 4.8767228765

65.7 131.4 4.1850989255 4.8782461061

65.8 131.6 4.1866198383 4.8797670189

65.9 131.8 4.1881384415 4.8812856221

66 132 4.189654742 4.8828019226

66.1 132.2 4.1911687469 4.8843159274

66.2 132.4 4.1926804629 4.8858276435

66.3 132.6 4.1941898972 4.8873370778

66.4 132.8 4.1956970565 4.888844237

66.5 133 4.1972019477 4.8903491282

66.6 133.2 4.1987045775 4.8918517581

66.7 133.4 4.2002049529 4.8933521335

66.8 133.6 4.2017030805 4.8948502611

66.9 133.8 4.2031989671 4.8963461477

67 134 4.2046926194 4.8978398

67.1 134.2 4.206184044 4.8993312245

67.2 134.4 4.2076732475 4.9008204281

67.3 134.6 4.2091602367 4.902307417267.4 134.8 4.2106450179 4.9037921985

67.5 135 4.2121275979 4.9052747784

67.6 135.2 4.213607983 4.9067551636

67.7 135.4 4.2150861799 4.9082333605

67.8 135.6 4.2165621949 4.9097093755

67.9 135.8 4.2180360346 4.9111832151

68 136 4.2195077052 4.9126548857

8/19/2019 y = ln (kx) / ln (k)

31/443

68.1 136.2 4.2209772132 4.9141243937

68.2 136.4 4.2224445648 4.9155917454

68.3 136.6 4.2239097666 4.9170569471

68.4 136.8 4.2253728246 4.9185200052

68.5 137 4.2268337453 4.9199809258

68.6 137.2 4.2282925347 4.9214397153

68.7 137.4 4.2297491992 4.9228963798

68.8 137.6 4.2312037449 4.9243509255

68.9 137.8 4.232656178 4.9258033586

69 138 4.2341065046 4.9272536852

69.1 138.2 4.2355547308 4.9287019113

69.2 138.4 4.2370008626 4.9301480432

69.3 138.6 4.2384449062 4.9315920868

69.4 138.8 4.2398868675 4.9330340481

69.5 139 4.2413267526 4.9344739331

69.6 139.2 4.2427645673 4.9359117479

69.7 139.4 4.2442003178 4.9373474983

69.8 139.6 4.2456340098 4.9387811903

69.9 139.8 4.2470656492 4.9402128298

70 140 4.248495242 4.9416424226

70.1 140.2 4.249922794 4.9430699746

70.2 140.4 4.251348311 4.9444954916

70.3 140.6 4.2527717988 4.9459189794

70.4 140.8 4.2541932632 4.9473404437

70.5 141 4.2556127098 4.9487598904

70.6 141.2 4.2570301445 4.9501773251

70.7 141.4 4.2584455729 4.9515927535

70.8 141.6 4.2598590007 4.9530061813

70.9 141.8 4.2612704335 4.9544176141

71 142 4.262679877 4.9558270576

71.1 142.2 4.2640873368 4.957234517471.2 142.4 4.2654928184 4.958639999

71.3 142.6 4.2668963274 4.960043508

71.4 142.8 4.2682978693 4.9614450499

71.5 143 4.2696974497 4.9628446303

71.6 143.2 4.271095074 4.9642422545

71.7 143.4 4.2724907476 4.9656379282

71.8 143.6 4.2738844761 4.9670316566

8/19/2019 y = ln (kx) / ln (k)

32/443

71.9 143.8 4.2752762647 4.9684234453

72 144 4.276666119 4.9698132996

72.1 144.2 4.2780540443 4.9712012249

72.2 144.4 4.2794400459 4.9725872265

72.3 144.6 4.2808241292 4.9739713097

72.4 144.8 4.2822062994 4.97535348

72.5 145 4.2835865619 4.9767337424

72.6 145.2 4.2849649218 4.9781121024

72.7 145.4 4.2863413845 4.9794885651

72.8 145.6 4.2877159552 4.9808631358

72.9 145.8 4.289088639 4.9822358196

73 146 4.2904594411 4.9836066217

73.1 146.2 4.2918283668 4.9849755473

73.2 146.4 4.293195421 4.9863426015

73.3 146.6 4.2945606089 4.9877077895

73.4 146.8 4.2959239356 4.9890711162

73.5 147 4.2972854062 4.9904325868

73.6 147.2 4.2986450257 4.9917922063

73.7 147.4 4.3000027992 4.9931499798

73.8 147.6 4.3013587316 4.9945059122

73.9 147.8 4.302712828 4.9958600085

74 148 4.3040650932 4.9972122738

74.1 148.2 4.3054155323 4.9985627129

74.2 148.4 4.3067641502 4.9999113307

74.3 148.6 4.3081109517 5.0012581323

74.4 148.8 4.3094559418 5.0026031224

74.5 149 4.3107991254 5.0039463059

74.6 149.2 4.3121405072 5.0052876878

74.7 149.4 4.3134800921 5.0066272727

74.8 149.6 4.314817885 5.0079650655

74.9 149.8 4.3161538905 5.009301071175 150 4.3174881135 5.0106352941

75.1 150.2 4.3188205588 5.0119677393

75.2 150.4 4.320151231 5.0132984115

75.3 150.6 4.3214801348 5.0146273154

75.4 150.8 4.322807275 5.0159544556

75.5 151 4.3241326563 5.0172798368

75.6 151.2 4.3254562832 5.0186034637

8/19/2019 y = ln (kx) / ln (k)

33/443

75.7 151.4 4.3267781604 5.019925341

75.8 151.6 4.3280982926 5.0212454732

75.9 151.8 4.3294166844 5.022563865

76 152 4.3307333403 5.0238805208

76.1 152.2 4.3320482649 5.0251954454

76.2 152.4 4.3333614627 5.0265086433

76.3 152.6 4.3346729383 5.0278201189

76.4 152.8 4.3359826962 5.0291298767

76.5 153 4.3372907408 5.0304379214

76.6 153.2 4.3385970767 5.0317442573

76.7 153.4 4.3399017084 5.0330488889

76.8 153.6 4.3412046402 5.0343518207

76.9 153.8 4.3425058765 5.0356530571

77 154 4.3438054219 5.0369526024

77.1 154.2 4.3451032806 5.0382504611

77.2 154.4 4.346399457 5.0395466376

77.3 154.6 4.3476939556 5.0408411362

77.4 154.8 4.3489867806 5.0421339612

77.5 155 4.3502779364 5.0434251169

77.6 155.2 4.3515674272 5.0447146077

77.7 155.4 4.3528552574 5.0460024379

77.8 155.6 4.3541414312 5.0472886117

77.9 155.8 4.3554259529 5.0485731334

78 156 4.3567088267 5.0498560072

78.1 156.2 4.3579900568 5.0511372374

78.2 156.4 4.3592696476 5.0524168281

78.3 156.6 4.360547603 5.0536947836

78.4 156.8 4.3618239274 5.0549711079

78.5 157 4.3630986248 5.0562458053

78.6 157.2 4.3643716994 5.05751888

78.7 157.4 4.3656431554 5.05879033678.8 157.6 4.3669129969 5.0600601774

78.9 157.8 4.3681812279 5.0613284084

79 158 4.3694478525 5.062595033

79.1 158.2 4.3707128748 5.0638600553

79.2 158.4 4.3719762988 5.0651234794

79.3 158.6 4.3732381286 5.0663853092

79.4 158.8 4.3744983683 5.0676455488

8/19/2019 y = ln (kx) / ln (k)

34/443

79.5 159 4.3757570217 5.0689042022

79.6 159.2 4.3770140929 5.0701612734

79.7 159.4 4.3782695858 5.0714167664

79.8 159.6 4.3795235045 5.072670685

79.9 159.8 4.3807758528 5.0739230333

80 160 4.3820266347 5.0751738152

80.1 160.2 4.3832758541 5.0764230346

80.2 160.4 4.3845235149 5.0776706954

80.3 160.6 4.385769621 5.0789168015

80.4 160.8 4.3870141762 5.0801613567

80.5 161 4.3882571844 5.081404365

80.6 161.2 4.3894986495 5.0826458301

80.7 161.4 4.3907385753 5.0838857558

80.8 161.6 4.3919769655 5.0851241461

80.9 161.8 4.3932138241 5.0863610046

81 162 4.3944491547 5.0875963352

81.1 162.2 4.3956829611 5.0888301417

81.2 162.4 4.3969152472 5.0900624277

81.3 162.6 4.3981460166 5.0912931971

81.4 162.8 4.399375273 5.0925224536

81.5 163 4.4006030202 5.0937502008

81.6 163.2 4.401829262 5.0949764425

81.7 163.4 4.4030540019 5.0962011824

81.8 163.6 4.4042772436 5.0974244242

81.9 163.8 4.4054989909 5.0986461714

82 164 4.4067192473 5.0998664278

82.1 164.2 4.4079380165 5.101085197

82.2 164.4 4.4091553021 5.1023024826

82.3 164.6 4.4103711077 5.1035182882

82.4 164.8 4.4115854369 5.1047326175

82.5 165 4.4127982933 5.105945473982.6 165.2 4.4140096805 5.1071568611

82.7 165.4 4.415219602 5.1083667826

82.8 165.6 4.4164280614 5.109575242

82.9 165.8 4.4176350621 5.1107822427

83 166 4.4188406078 5.1119877884

83.1 166.2 4.4200447019 5.1131918824

83.2 166.4 4.4212473478 5.1143945284

8/19/2019 y = ln (kx) / ln (k)

35/443

83.3 166.6 4.4224485492 5.1155957297

83.4 166.8 4.4236483094 5.1167954899

83.5 167 4.4248466319 5.1179938124

83.6 167.2 4.4260435201 5.1191907007

83.7 167.4 4.4272389775 5.1203861581

83.8 167.6 4.4284330075 5.121580188

83.9 167.8 4.4296256135 5.122772794

84 168 4.4308167988 5.1239639794

84.1 168.2 4.432006567 5.1251537475

84.2 168.4 4.4331949212 5.1263421018

84.3 168.6 4.434381865 5.1275290456

84.4 168.8 4.4355674016 5.1287145822

84.5 169 4.4367515344 5.1298987149

84.6 169.2 4.4379342666 5.1310814472

84.7 169.4 4.4391156017 5.1322627822

84.8 169.6 4.4402955428 5.1334427234

84.9 169.8 4.4414740933 5.1346212739

85 170 4.4426512565 5.1357984371

85.1 170.2 4.4438270356 5.1369742161

85.2 170.4 4.4450014338 5.1381486144

85.3 170.6 4.4461744545 5.1393216351

85.4 170.8 4.4473461008 5.1404932814

85.5 171 4.4485163759 5.1416635565

85.6 171.2 4.4496852831 5.1428324637

85.7 171.4 4.4508528256 5.1440000062

85.8 171.6 4.4520190065 5.1451661871

85.9 171.8 4.453183829 5.1463310096

86 172 4.4543472963 5.1474944768

86.1 172.2 4.4555094114 5.148656592

86.2 172.4 4.4566701777 5.1498173582

86.3 172.6 4.4578295981 5.150976778686.4 172.8 4.4589876758 5.1521348564

86.5 173 4.4601444139 5.1532915945

86.6 173.2 4.4612998156 5.1544469961

86.7 173.4 4.4624538838 5.1556010643

86.8 173.6 4.4636066217 5.1567538022

86.9 173.8 4.4647580323 5.1579052128

87 174 4.4659081187 5.1590552992

8/19/2019 y = ln (kx) / ln (k)

36/443

87.1 174.2 4.4670568839 5.1602040644

87.2 174.4 4.4682043309 5.1613515115

87.3 174.6 4.4693504628 5.1624976434

87.4 174.8 4.4704952827 5.1636424632

87.5 175 4.4716387934 5.1647859739

87.6 175.2 4.4727809979 5.1659281785

87.7 175.4 4.4739218994 5.1670690799

87.8 175.6 4.4750615006 5.1682086812

87.9 175.8 4.4761998047 5.1693469853

88 176 4.4773368145 5.170483995

88.1 176.2 4.4784725329 5.1716197135

88.2 176.4 4.479606963 5.1727541436

88.3 176.6 4.4807401076 5.1738872882

88.4 176.8 4.4818719696 5.1750191502

88.5 177 4.483002552 5.1761497326

88.6 177.2 4.4841318576 5.1772790382

88.7 177.4 4.4852598893 5.1784070699

88.8 177.6 4.48638665 5.1795338306

88.9 177.8 4.4875121425 5.1806593231

89 178 4.4886363697 5.1817835503

89.1 178.2 4.4897593345 5.182906515

89.2 178.4 4.4908810396 5.1840282201

89.3 178.6 4.4920014879 5.1851486684

89.4 178.8 4.4931206822 5.1862678627

89.5 179 4.4942386253 5.1873858058

89.6 179.2 4.49535532 5.1885025005

89.7 179.4 4.4964707691 5.1896179496

89.8 179.6 4.4975849753 5.1907321559

89.9 179.8 4.4986979415 5.191845122

90 180 4.4998096703 5.1929568509

90.1 180.2 4.5009201646 5.194067345290.2 180.4 4.5020294271 5.1951766076

90.3 180.6 4.5031374604 5.196284641

90.4 180.8 4.5042442674 5.197391448

90.5 181 4.5053498507 5.1984970313

90.6 181.2 4.506454213 5.1996013936

90.7 181.4 4.5075573571 5.2007045377

90.8 181.6 4.5086592856 5.2018064662

8/19/2019 y = ln (kx) / ln (k)

37/443

90.9 181.8 4.5097600012 5.2029071817

91 182 4.5108595065 5.2040066871

91.1 182.2 4.5119578043 5.2051049848

91.2 182.4 4.5130548971 5.2062020776

91.3 182.6 4.5141507876 5.2072979682

91.4 182.8 4.5152454785 5.208392659

91.5 183 4.5163389723 5.2094861528

91.6 183.2 4.5174312717 5.2105784522

91.7 183.4 4.5185223793 5.2116695598

91.8 183.6 4.5196122976 5.2127594782

91.9 183.8 4.5207010294 5.2138482099

92 184 4.521788577 5.2149357576

92.1 184.2 4.5228749433 5.2160221238

92.2 184.4 4.5239601306 5.2171073111

92.3 184.6 4.5250441415 5.2181913221

92.4 184.8 4.5261269786 5.2192741592

92.5 185 4.5272086445 5.2203558251

92.6 185.2 4.5282891417 5.2214363222

92.7 185.4 4.5293684726 5.2225156531

92.8 185.6 4.5304466398 5.2235938204

92.9 185.8 4.5315236458 5.2246708264

93 186 4.5325994932 5.2257466737

93.1 186.2 4.5336741843 5.2268213648

93.2 186.4 4.5347477217 5.2278949023

93.3 186.6 4.5358201079 5.2289672884

93.4 186.8 4.5368913452 5.2300385258

93.5 187 4.5379614363 5.2311086169

93.6 187.2 4.5390303835 5.232177564

93.7 187.4 4.5400981892 5.2332453698

93.8 187.6 4.541164856 5.2343120366

93.9 187.8 4.5422303862 5.235377566894 188 4.5432947823 5.2364419628

94.1 188.2 4.5443580466 5.2375052272

94.2 188.4 4.5454201816 5.2385673621

94.3 188.6 4.5464811896 5.2396283702

94.4 188.8 4.5475410732 5.2406882537

94.5 189 4.5485998345 5.2417470151

94.6 189.2 4.5496574761 5.2428046566

8/19/2019 y = ln (kx) / ln (k)

38/443

94.7 189.4 4.5507140002 5.2438611808

94.8 189.6 4.5517694093 5.2449165898

94.9 189.8 4.5528237056 5.2459708862

95 190 4.5538768916 5.2470240722

95.1 190.2 4.5549289696 5.2480761501

95.2 190.4 4.5559799418 5.2491271224

95.3 190.6 4.5570298107 5.2501769912

95.4 190.8 4.5580785785 5.251225759

95.5 191 4.5591262475 5.252273428

95.6 191.2 4.5601728201 5.2533200006

95.7 191.4 4.5612182985 5.254365479

95.8 191.6 4.562262685 5.2554098655

95.9 191.8 4.5633059819 5.2564531624

96 192 4.5643481915 5.257495372

96.1 192.2 4.565389316 5.2585364965

96.2 192.4 4.5664293577 5.2595765382

96.3 192.6 4.5674683188 5.2606154994

96.4 192.8 4.5685062016 5.2616533822

96.5 193 4.5695430083 5.2626901889

96.6 193.2 4.5705787412 5.2637259218

96.7 193.4 4.5716134025 5.264760583

96.8 193.6 4.5726469943 5.2657941748

96.9 193.8 4.5736795189 5.2668266995

97 194 4.5747109785 5.2678581591

97.1 194.2 4.5757413753 5.2688885559

97.2 194.4 4.5767707115 5.269917892

97.3 194.6 4.5777989892 5.2709461698

97.4 194.8 4.5788262106 5.2719733912

97.5 195 4.579852378 5.2729995586

97.6 195.2 4.5808774934 5.274024674

97.7 195.4 4.581901559 5.275048739697.8 195.6 4.582924577 5.2760717576

97.9 195.8 4.5839465495 5.2770937301

98 196 4.5849674787 5.2781146592

98.1 196.2 4.5859873666 5.2791345471

98.2 196.4 4.5870062154 5.2801533959

98.3 196.6 4.5880240272 5.2811712077

98.4 196.8 4.5890408041 5.2821879846

8/19/2019 y = ln (kx) / ln (k)

39/443

98.5 197 4.5900565482 5.2832037287

98.6 197.2 4.5910712616 5.2842184422

98.7 197.4 4.5920849464 5.285232127

98.8 197.6 4.5930976048 5.2862447853

98.9 197.8 4.5941092386 5.2872564192

99 198 4.5951198501 5.2882670307

99.1 198.2 4.5961294413 5.2892766219

99.2 198.4 4.5971380143 5.2902851949

99.3 198.6 4.5981455711 5.2912927516

99.4 198.8 4.5991521137 5.2922992942

99.5 199 4.6001576442 5.2933048247

99.6 199.2 4.6011621646 5.2943093452

99.7 199.4 4.602165677 5.2953128575

99.8 199.6 4.6031681833 5.2963153639

99.9 199.8 4.6041696857 5.2973168662

100 200 4.605170186 5.2983173665

8/19/2019 y = ln (kx) / ln (k)

40/443

   A^n (=2A)

0 1

0.6989700043 0.2

0.5693234419 0.4

0.4242833575 0.6

0.2435292026 0.8

0 1

-0.3569154489 1.2

-0.9433582099 1.4

-2.1062837195 1.6

-5.578813479 1.8

#DIV/0 #DIV/0

8.2725408973 2.2

4.8017840169 2.4

3.6419267958 2.6

3.0600427171 2.8

2.7095112914 3

2.4747698474 3.2

2.3062764359 3.4

2.1792495848 3.6

2.079914285 3.8

2 4

1.9342395089 4.2

1.8791181558 4.4

1.8322002503 4.6

1.7917440692 4.8

1.7564707974 5

1.7254200713 5.2

1.6978564745 5.41.6732071764 5.6

1.6510192454 5.8

1.6309297536 6

1.6126444113 6.2

1.5959220204 6.4

1.5805629753 6.6

1.5664006342 6.8

0 20

-8

-6

-4

-2

0

2

4

6

8

10

8/19/2019 y = ln (kx) / ln (k)

41/443

1.5532947557 7

1.5411264469 7.2

1.5297942314 7.4

1.5192109563 7.6

1.5093013388 7.8

1.5 8

1.4912498793 8.2

1.4830009441 8.4

1.4752091332 8.6

1.4678354861 8.8

1.4608454206 9

1.4542081304 9.2

1.4478960796 9.4

1.4418845765 9.6

1.4361514132 9.8

1.4306765581 10

1.4254418937 10.2

1.4204309915 10.4

1.4156289175 10.6

1.4110220651 10.8

1.4065980092 11

1.4023453795 11.2

1.3982537498 11.4

1.3943135413 11.6

1.3905159371 11.8

1.3868528072 12

1.3833166426 12.2

1.3799004957 12.4

1.3765979292 12.6

1.3734029688 12.8

1.3703100622 131.3673140421 13.2

1.364410093 13.4

1.3615937212 13.6

1.3588607283 13.8

1.3562071871 14

1.3536294195 14.2

1.3511239769 14.4

8/19/2019 y = ln (kx) / ln (k)

42/443

1.3486876226 14.6

1.3463173154 14.8

1.3440101948 15

1.3417635676 15.2

1.3395748958 15.4

1.3374417856 15.6

1.3353619767 15.8

1.3333333333 16

1.3313538357 16.2

1.3294215719 16.4

1.3275347309 16.6

1.3256915958 16.8

1.3238905378 17

1.3221300102 17.2

1.3204085439 17.4

1.3187247416 17.6

1.3170772744 17.8

1.3154648768 18

1.3138863433 18.2

1.3123405247 18.4

1.3108263249 18.6

1.3093426979 18.8

1.3078886446 19

1.3064632105 19.2

1.3050654829 19.4

1.303694589 19.6

1.3023496932 19.8

1.3010299957 20

1.2997347299 20.2

1.2984631612 20.4

1.2972145852 20.61.2959883261 20.8

1.2947837349 21

1.2936001888 21.2

1.2924370892 21.4

1.2912938609 21.6

1.2901699506 21.8

1.2890648263 22

8/19/2019 y = ln (kx) / ln (k)

43/443

1.287977976 22.2

1.2869089066 22.4

1.2858571434 22.6

1.2848222291 22.8

1.2838037226 23

1.282801199 23.2

1.2818142483 23.4

1.2808424748 23.6

1.2798854968 23.8

1.2789429457 24

1.2780144652 24.2

1.2770997115 24.4

1.276198352 24.6

1.2753100654 24.8

1.2744345408 25

1.2735714774 25.2

1.2727205842 25.4

1.2718815798 25.6

1.2710541912 25.8

1.2702381544 26

1.2694332136 26.2

1.2686391208 26.4

1.2678556356 26.6

1.2670825252 26.8

1.2663195633 27

1.265566531 27.2

1.2648232155 27.4

1.2640894102 27.6

1.263364915 27.8

1.262649535 28

1.2619430815 28.21.2612453707 28.4

1.2605562243 28.6

1.2598754688 28.8

1.2592029357 29

1.2585384612 29.2

1.2578818858 29.4

1.2572330545 29.6

8/19/2019 y = ln (kx) / ln (k)

44/443

1.2565918165 29.8

1.2559580248 30

1.2553315367 30.2

1.254712213 30.4

1.2540999182 30.6

1.2534945205 30.8

1.2528958912 31

1.2523039053 31.2

1.2517184406 31.4

1.2511393783 31.6

1.2505666025 31.8

1.25 32

1.2494394607 32.2

1.248884877 32.4

1.2483361441 32.6

1.2477931597 32.8

1.2472558239 33

1.2467240391 33.2

1.2461977104 33.4

1.2456767448 33.6

1.2451610515 33.8

1.2446505421 34

1.24414513 34.2

1.2436447307 34.4

1.2431492615 34.6

1.2426586418 34.8

1.2421727927 35

1.2416916371 35.2

1.2412150995 35.4

1.2407431064 35.6

1.2402755856 35.81.2398124666 36

1.2393536804 36.2

1.2388991596 36.4

1.2384488382 36.6

1.2380026516 36.8

1.2375605365 37

1.2371224311 37.2

8/19/2019 y = ln (kx) / ln (k)

45/443

1.2366882748 37.4

1.2362580083 37.6

1.2358315734 37.8

1.2354089134 38

1.2349899724 38.2

1.2345746961 38.4

1.2341630307 38.6

1.2337549241 38.8

1.2333503249 39

1.2329491827 39.2

1.2325514483 39.4

1.2321570733 39.6

1.2317660104 39.8

1.2313782132 40

1.230993636 40.2

1.2306122342 40.4

1.230233964 40.6

1.2298587824 40.8

1.2294866473 41

1.2291175174 41.2

1.228751352 41.4

1.2283881113 41.6

1.2280277563 41.8

1.2276702487 42

1.2273155507 42.2

1.2269636255 42.4

1.2266144368 42.6

1.2262679489 42.8

1.2259241269 43

1.2255829364 43.2

1.2252443437 43.41.2249083157 43.6

1.2245748199 43.8

1.2242438242 44

1.2239152973 44.2

1.2235892083 44.4

1.2232655269 44.6

1.2229442233 44.8

8/19/2019 y = ln (kx) / ln (k)

46/443

1.2226252681 45

1.2223086327 45.2

1.2219942887 45.4

1.2216822083 45.6

1.2213723642 45.8

1.2210647295 46

1.2207592776 46.2

1.2204559828 46.4

1.2201548193 46.6

1.219855762 46.8

1.2195587862 47

1.2192638676 47.2

1.2189709822 47.4

1.2186801066 47.6

1.2183912174 47.8

1.218104292 48

1.2178193079 48.2

1.217536243 48.4

1.2172550756 48.6

1.2169757843 48.8

1.2166983481 49

1.2164227462 49.2

1.2161489583 49.4

1.2158769643 49.6

1.2156067443 49.8

1.215338279 50

1.2150715492 50.2

1.214806536 50.4

1.2145432207 50.6

1.2142815851 50.8

1.2140216112 511.2137632812 51.2

1.2135065775 51.4

1.213251483 51.6

1.2129979806 51.8

1.2127460536 52

1.2124956855 52.2

1.21224686 52.4

8/19/2019 y = ln (kx) / ln (k)

47/443

1.2119995612 52.6

1.2117537733 52.8

1.2115094807 53

1.211266668 53.2

1.2110253202 53.4

1.2107854223 53.6

1.2105469597 53.8

1.2103099179 54

1.2100742825 54.2

1.2098400396 54.4

1.2096071753 54.6

1.2093756758 54.8

1.2091455276 55

1.2089167175 55.2

1.2086892323 55.4

1.2084630591 55.6

1.2082381851 55.8

1.2080145977 56

1.2077922844 56.2

1.2075712331 56.4

1.2073514315 56.6

1.2071328678 56.8

1.2069155303 57

1.2066994072 57.2

1.2064844871 57.4

1.2062707587 57.6

1.2060582108 57.8

1.2058468325 58

1.2056366127 58.2

1.2054275409 58.4

1.2052196064 58.61.2050127987 58.8

1.2048071075 59

1.2046025227 59.2

1.2043990341 59.4

1.2041966318 59.6

1.203995306 59.8

1.2037950471 60

8/19/2019 y = ln (kx) / ln (k)

48/443

1.2035958454 60.2

1.2033976915 60.4

1.2032005762 60.6

1.2030044901 60.8

1.2028094241 61

1.2026153694 61.2

1.202422317 61.4

1.2022302581 61.6

1.2020391842 61.8

1.2018490866 62

1.2016599569 62.2

1.2014717867 62.4

1.2012845678 62.6

1.2010982921 62.8

1.2009129515 63

1.2007285381 63.2

1.2005450439 63.4

1.2003624613 63.6

1.2001807825 63.8

1.2 64

1.1998201063 64.2

1.1996410939 64.4

1.1994629556 64.6

1.1992856841 64.8

1.1991092722 65

1.1989337129 65.2

1.1987589993 65.4

1.1985851243 65.6

1.1984120812 65.8

1.1982398632 66

1.1980684636 66.21.1978978759 66.4

1.1977280934 66.6

1.1975591099 66.8

1.1973909188 67

1.1972235139 67.2

1.1970568889 67.4

1.1968910377 67.6

8/19/2019 y = ln (kx) / ln (k)

49/443

1.1967259541 67.8

1.1965616322 68

1.196398066 68.2

1.1962352495 68.4

1.1960731769 68.6

1.1959118425 68.8

1.1957512406 69

1.1955913654 69.2

1.1954322115 69.4

1.1952737732 69.6

1.1951160451 69.8

1.1949590219 70

1.1948026981 70.2

1.1946470684 70.4

1.1944921277 70.6

1.1943378707 70.8

1.1941842923 71

1.1940313874 71.2

1.1938791511 71.4

1.1937275783 71.6

1.1935766641 71.8

1.1934264036 72

1.1932767921 72.2

1.1931278248 72.4

1.1929794969 72.6

1.1928318038 72.8

1.1926847408 73

1.1925383035 73.2

1.1923924872 73.4

1.1922472874 73.6

1.1921026998 73.81.19195872 74

1.1918153436 74.2

1.1916725662 74.4

1.1915303837 74.6

1.1913887918 74.8

1.1912477864 75

1.1911073632 75.2

8/19/2019 y = ln (kx) / ln (k)

50/443

1.1909675183 75.4

1.1908282475 75.6

1.1906895469 75.8

1.1905514124 76

1.1904138402 76.2

1.1902768263 76.4

1.1901403668 76.6

1.1900044581 76.8

1.1898690961 77

1.1897342773 77.2

1.1895999979 77.4

1.1894662542 77.6

1.1893330426 77.8

1.1892003595 78

1.1890682013 78.2

1.1889365644 78.4

1.1888054454 78.6

1.1886748408 78.8

1.1885447471 79

1.188415161 79.2

1.188286079 79.4

1.1881574978 79.6

1.1880294142 79.8

1.1879018247 80

1.1877747262 80.2

1.1876481155 80.4

1.1875219893 80.6

1.1873963445 80.8

1.1872711779 81

1.1871464865 81.2

1.1870222672 81.41.1868985169 81.6

1.1867752326 81.8

1.1866524112 82

1.18653005 82.2

1.1864081458 82.4

1.1862866958 82.6

1.1861656971 82.8

8/19/2019 y = ln (kx) / ln (k)

51/443

1.1860451468 83

1.1859250421 83.2

1.1858053802 83.4

1.1856861583 83.6

1.1855673736 83.8

1.1854490234 84

1.185331105 84.2

1.1852136157 84.4

1.1850965528 84.6

1.1849799137 84.8

1.1848636957 85

1.1847478963 85.2

1.1846325129 85.4

1.1845175429 85.6

1.1844029838 85.8

1.1842888331 86

1.1841750884 86.2

1.184061747 86.4

1.1839488067 86.6

1.1838362649 86.8

1.1837241193 87

1.1836123674 87.2

1.183501007 87.4

1.1833900357 87.6

1.1832794511 87.8

1.1831692509 88

1.1830594329 88.2

1.1829499948 88.4

1.1828409344 88.6

1.1827322493 88.8

1.1826239375 891.1825159967 89.2

1.1824084248 89.4

1.1823012195 89.6

1.1821943788 89.8

1.1820879005 90

1.1819817825 90.2

1.1818760228 90.4

8/19/2019 y = ln (kx) / ln (k)

52/443

1.1817706192 90.6

1.1816655698 90.8

1.1815608724 91

1.1814565251 91.2

1.1813525259 91.4

1.1812488727 91.6

1.1811455637 91.8

1.1810425968 92

1.1809399701 92.2

1.1808376817 92.4

1.1807357296 92.6

1.1806341121 92.8

1.1805328271 93

1.1804318729 93.2

1.1803312476 93.4

1.1802309493 93.6

1.1801309763 93.8

1.1800313267 94

1.1799319987 94.2

1.1798329906 94.4

1.1797343006 94.6

1.1796359269 94.8

1.1795378678 95

1.1794401216 95.2

1.1793426866 95.4

1.1792455611 95.6

1.1791487434 95.8

1.1790522318 96

1.1789560246 96.2

1.1788601203 96.4

1.1787645171 96.61.1786692135 96.8

1.1785742079 97

1.1784794986 97.2

1.1783850841 97.4

1.1782909628 97.6

1.1781971331 97.8

1.1781035936 98

8/19/2019 y = ln (kx) / ln (k)

53/443

1.1780103425 98.2

1.1779173785 98.4

1.1778247001 98.6

1.1777323056 98.8

1.1776401936 99

1.1775483627 99.2

1.1774568114 99.4

1.1773655381 99.6

1.1772745415 99.8

1.1771838201 100

1.1770933726 100.2

1.1770031973 100.4

1.1769132931 100.6

1.1768236584 100.8

1.1767342919 101

1.1766451922 101.2

1.176556358 101.4

1.1764677878 101.6

1.1763794804 101.8

1.1762914344 102

1.1762036484 102.2

1.1761161212 102.4

1.1760288515 102.6

1.1759418379 102.8

1.1758550791 103

1.1757685739 103.2

1.175682321 103.4

1.1755963192 103.6

1.1755105671 103.8

1.1754250636 104

1.1753398074 104.21.1752547972 104.4

1.1751700319 104.6

1.1750855102 104.8

1.175001231 105

1.1749171931 105.2

1.1748333952 105.4

1.1747498361 105.6

8/19/2019 y = ln (kx) / ln (k)

54/443

1.1746665148 105.8

1.17458343 106

1.1745005807 106.2

1.1744179656 106.4

1.1743355836 106.6

1.1742534336 106.8

1.1741715144 107

1.174089825 107.2

1.1740083643 107.4

1.173927131 107.6

1.1738461243 107.8

1.1737653429 108

1.1736847858 108.2

1.1736044519 108.4

1.1735243401 108.6

1.1734444495 108.8

1.1733647789 109

1.1732853273 109.2

1.1732060937 109.4

1.173127077 109.6

1.1730482763 109.8

1.1729696904 110

1.1728913185 110.2

1.1728131595 110.4

1.1727352124 110.6

1.1726574762 110.8

1.1725799499 111

1.1725026326 111.2

1.1724255233 111.4

1.172348621 111.6

1.1722719249 111.81.1721954338 112

1.1721191469 112.2

1.1720430633 112.4

1.171967182 112.6

1.171891502 112.8

1.1718160226 113

1.1717407427 113.2

8/19/2019 y = ln (kx) / ln (k)

55/443

1.1716656614 113.4

1.1715907779 113.6

1.1715160913 113.8

1.1714416006 114

1.171367305 114.2

1.1712932035 114.4

1.1712192954 114.6

1.1711455798 114.8

1.1710720558 115

1.1709987225 115.2

1.170925579 115.4

1.1708526247 115.6

1.1707798585 115.8

1.1707072797 116

1.1706348874 116.2

1.1705626808 116.4

1.1704906591 116.6

1.1704188215 116.8

1.1703471671 117

1.1702756952 117.2

1.170204405 117.4

1.1701332956 117.6

1.1700623663 117.8

1.1699916163 118

1.1699210448 118.2

1.169850651 118.4

1.1697804342 118.6

1.1697103936 118.8

1.1696405284 119

1.1695708379 119.2

1.1695013213 119.41.1694319779 119.6

1.1693628069 119.8

1.1692938076 120

1.1692249793 120.2

1.1691563212 120.4

1.1690878326 120.6

1.1690195128 120.8

8/19/2019 y = ln (kx) / ln (k)

56/443

1.1689513611 121

1.1688833767 121.2

1.168815559 121.4

1.1687479072 121.6

1.1686804207 121.8

1.1686130987 122

1.1685459406 122.2

1.1684789456 122.4

1.1684121131 122.6

1.1683454425 122.8

1.168278933 123

1.1682125839 123.2

1.1681463946 123.4

1.1680803645 123.6

1.1680144928 123.8

1.167948779 124

1.1678832223 124.2

1.1678178221 124.4

1.1677525778 124.6

1.1676874887 124.8

1.1676225543 125

1.1675577738 125.2

1.1674931466 125.4

1.1674286721 125.6

1.1673643497 125.8

1.1673001788 126

1.1672361587 126.2

1.1671722889 126.4

1.1671085687 126.6

1.1670449975 126.8

1.1669815748 1271.1669182999 127.2

1.1668551722 127.4

1.1667921912 127.6

1.1667293562 127.8

1.1666666667 128

1.166604122 128.2

1.1665417217 128.4

8/19/2019 y = ln (kx) / ln (k)

57/443

1.1664794652 128.6

1.1664173517 128.8

1.1663553809 129

1.1662935522 129.2

1.1662318649 129.4

1.1661703185 129.6

1.1661089124 129.8

1.1660476462 130

1.1659865192 130.2

1.165925531 130.4

1.1658646809 130.6

1.1658039684 130.8

1.1657433931 131

1.1656829542 131.2

1.1656226514 131.4

1.1655624841 131.6

1.1655024518 131.8

1.1654425539 132

1.16538279 132.2

1.1653231594 132.4

1.1652636618 132.6

1.1652042965 132.8

1.1651450631 133

1.1650859611 133.2

1.16502699 133.4

1.1649681492 133.6

1.1649094383 133.8

1.1648508567 134

1.1647924041 134.2

1.1647340798 134.4

1.1646758835 134.61.1646178145 134.8

1.1645598725 135

1.164502057 135.2

1.1644443674 135.4

1.1643868034 135.6

1.1643293644 135.8

1.16427205 136

8/19/2019 y = ln (kx) / ln (k)

58/443

1.1642148596 136.2

1.1641577929 136.4

1.1641008494 136.6

1.1640440286 136.8

1.1639873301 137

1.1639307533 137.2

1.163874298 137.4

1.1638179635 137.6

1.1637617495 137.8

1.1637056554 138

1.163649681 138.2

1.1635938257 138.4

1.1635380891 138.6

1.1634824707 138.8

1.1634269701 139

1.163371587 139.2

1.1633163208 139.4

1.1632611711 139.6

1.1632061376 139.8

1.1631512197 140

1.1630964171 140.2

1.1630417293 140.4

1.162987156 140.6

1.1629326967 140.8

1.162878351 141

1.1628241185 141.2

1.1627699987 141.4

1.1627159914 141.6

1.1626620961 141.8

1.1626083123 142

1.1625546397 142.21.1625010779 142.4

1.1624476264 142.6

1.162394285 142.8

1.1623410531 143

1.1622879305 143.2

1.1622349167 143.4

1.1621820113 143.6

8/19/2019 y = ln (kx) / ln (k)

59/443

1.162129214 143.8

1.1620765244 144

1.1620239421 144.2

1.1619714666 144.4

1.1619190977 144.6

1.161866835 144.8

1.1618146781 145

1.1617626266 145.2

1.1617106801 145.4

1.1616588384 145.6

1.1616071009 145.8

1.1615554674 146

1.1615039376 146.2

1.1614525109 146.4

1.1614011871 146.6

1.1613499659 146.8

1.1612988468 147

1.1612478296 147.2

1.1611969138 147.4

1.1611460991 147.6

1.1610953852 147.8

1.1610447718 148

1.1609942584 148.2

1.1609438447 148.4

1.1608935304 148.6

1.1608433152 148.8

1.1607931988 149

1.1607431807 149.2

1.1606932606 149.4

1.1606434383 149.6

1.1605937133 149.81.1605440854 150

1.1604945543 150.2

1.1604451195 150.4

1.1603957808 150.6

1.1603465379 150.8

1.1602973904 151

1.160248338 151.2

8/19/2019 y = ln (kx) / ln (k)

60/443

1.1601993804 151.4

1.1601505173 151.6

1.1601017484 151.8

1.1600530733 152

1.1600044917 152.2

1.1599560033 152.4

1.1599076079 152.6

1.1598593051 152.8

1.1598110945 153

1.159762976 153.2

1.1597149491 153.4

1.1596670137 153.6

1.1596191693 153.8

1.1595714157 154

1.1595237526 154.2

1.1594761796 154.4

1.1594286966 154.6

1.1593813032 154.8

1.159333999 155

1.1592867839 155.2

1.1592396576 155.4

1.1591926196 155.6

1.1591456698 155.8

1.1590988079 156

1.1590520335 156.2

1.1590053464 156.4

1.1589587464 156.6

1.1589122331 156.8

1.1588658062 157

1.1588194655 157.2

1.1587732107 157.41.1587270415 157.6

1.1586809577 157.8

1.1586349589 158

1.1585890449 158.2

1.1585432155 158.4

1.1584974703 158.6

1.1584518091 158.8

8/19/2019 y = ln (kx) / ln (k)

61/443

1.1584062317 159

1.1583607377 159.2

1.1583153269 159.4

1.158269999 159.6

1.1582247538 159.8

1.1581795909 160

1.1581345103 160.2

1.1580895115 160.4

1.1580445943 160.6

1.1579997585 160.8

1.1579550039 161

1.1579103301 161.2

1.1578657369 161.4

1.157821224 161.6

1.1577767913 161.8

1.1577324384 162

1.1576881651 162.2

1.1576439712 162.4

1.1575998564 162.6

1.1575558204 162.8

1.1575118631 163

1.1574679842 163.2

1.1574241834 163.4

1.1573804605 163.6

1.1573368152 163.8

1.1572932473 164

1.1572497567 164.2

1.157206343 164.4

1.1571630059 164.6

1.1571197454 164.8

1.1570765611 1651.1570334527 165.2

1.1569904202 165.4

1.1569474632 165.6

1.1569045815 165.8

1.1568617749 166

1.1568190431 166.2

1.1567763859 166.4

8/19/2019 y = ln (kx) / ln (k)

62/443

1.1567338032 166.6

1.1566912946 166.8

1.15664886 167

1.1566064991 167.2

1.1565642117 167.4

1.1565219976 167.6

1.1564798565 167.8

1.1564377883 168

1.1563957928 168.2

1.1563538696 168.4

1.1563120186 168.6

1.1562702396 168.8

1.1562285323 169

1.1561868966 169.2

1.1561453323 169.4

1.156103839 169.6

1.1560624167 169.8

1.156021065 170

1.1559797839 170.2

1.155938573 170.4

1.1558974322 170.6

1.1558563613 170.8

1.15581536 171

1.1557744282 171.2

1.1557335656 171.4

1.1556927721 171.6

1.1556520474 171.8

1.1556113914 172

1.1555708038 172.2

1.1555302845 172.4

1.1554898332 172.61.1554494497 172.8

1.1554091339 173

1.1553688856 173.2

1.1553287045 173.4

1.1552885904 173.6

1.1552485433 173.8

1.1552085628 174

8/19/2019 y = ln (kx) / ln (k)

63/443

1.1551686488 174.2

1.155128801 174.4

1.1550890194 174.6

1.1550493037 174.8

1.1550096536 175

1.1549700692 175.2

1.15493055 175.4

1.154891096 175.6

1.154851707 175.8

1.1548123827 176

1.1547731231 176.2

1.1547339278 176.4

1.1546947968 176.6

1.1546557299 176.8

1.1546167267 177

1.1545777873 177.2

1.1545389114 177.4

1.1545000988 177.6

1.1544613493 177.8

1.1544226628 178

1.1543840391 178.2

1.154345478 178.4

1.1543069793 178.6

1.1542685429 178.8

1.1542301685 179

1.1541918561 179.2

1.1541536054 179.4

1.1541154162 179.6

1.1540772885 179.8

1.154039222 180

1.1540012165 180.21.1539632719 180.4

1.1539253879 180.6

1.1538875646 180.8

1.1538498016 181

1.1538120988 181.2

1.153774456 181.4

1.1537368731 181.6

8/19/2019 y = ln (kx) / ln (k)

64/443

1.1536993499 181.8

1.1536618863 182

1.153624482 182.2

1.153587137 182.4

1.1535498509 182.6

1.1535126238 182.8

1.1534754554 183

1.1534383456 183.2

1.1534012941 183.4

1.1533643009 183.6

1.1533273658 183.8

1.1532904887 184

1.1532536692 184.2

1.1532169074 184.4

1.1531802031 184.6

1.153143556 184.8

1.1531069661 185

1.1530704332 185.2

1.1530339571 185.4

1.1529975377 185.6

1.1529611748 185.8

1.1529248683 186

1.152888618 186.2

1.1528524238 186.4

1.1528162855 186.6

1.152780203 186.8

1.1527441761 187

1.1527082046 187.2

1.1526722885 187.4

1.1526364276 187.6

1.1526006216 187.81.1525648706 188

1.1525291743 188.2

1.1524935326 188.4

1.1524579453 188.6

1.1524224123 188.8

1.1523869335 189

1.1523515087 189.2

8/19/2019 y = ln (kx) / ln (k)

65/443

1.1523161378 189.4

1.1522808205 189.6

1.1522455569 189.8

1.1522103467 190

1.1521751898 190.2

1.1521400861 190.4

1.1521050354 190.6

1.1520700375 190.8

1.1520350925 191

1.1520002 191.2

1.15196536 191.4

1.1519305723 191.6

1.1518958368 191.8

1.1518611533 192

1.1518265218 192.2

1.1517919421 192.4

1.151757414 192.6

1.1517229374 192.8

1.1516885122 193

1.1516541383 193.2

1.1516198155 193.4

1.1515855437 193.6

1.1515513227 193.8

1.1515171524 194

1.1514830327 194.2

1.1514489635 194.4

1.1514149446 194.6

1.151380976 194.8

1.1513470574 195

1.1513131887 195.2

1.1512793698 195.41.1512456007 195.6

1.1512118811 195.8

1.1511782109 196

1.1511445901 196.2

1.1511110184 196.4

1.1510774958 196.6

1.1510440221 196.8

8/19/2019 y = ln (kx) / ln (k)

66/443

1.1510105972 197

1.150977221 197.2

1.1509438934 197.4

1.1509106142 197.6

1.1508773833 197.8

1.1508442006 198

1.150811066 198.2

1.1507779793 198.4

1.1507449405 198.6

1.1507119494 198.8

1.1506790058 199

1.1506461098 199.2

1.1506132611 199.4

1.1505804596 199.6

1.1505477052 199.8

1.1505149978 200

8/19/2019 y = ln (kx) / ln (k)

67/443

40 60 80

n vs. A

8/19/2019 y = ln (kx) / ln (k)

68/443

8/19/2019 y = ln (kx) / ln (k)

69/443

8/19/2019 y = ln (kx) / ln (k)

70/443

8/19/2019 y = ln (kx) / ln (k)

71/443

8/19/2019 y = ln (kx) / ln (k)

72/443

8/19/2019 y = ln (kx) / ln (k)

73/443

8/19/2019 y = ln (kx) / ln (k)

74/443

8/19/2019 y = ln (kx) / ln (k)

75/443

8/19/2019 y = ln (kx) / ln (k)

76/443

8/19/2019 y = ln (kx) / ln (k)

77/443

8/19/2019 y = ln (kx) / ln (k)

78/443

8/19/2019 y = ln (kx) / ln (k)

79/443

8/19/2019 y = ln (kx) / ln (k)

80/443

8/19/2019 y = ln (kx) / ln (k)

81/443

8/19/2019 y = ln (kx) / ln (k)

82/443

8/19/2019 y = ln (kx) / ln (k)

83/443

8/19/2019 y = ln (kx) / ln (k)

84/443

8/19/2019 y = ln (kx) / ln (k)

85/443

8/19/2019 y = ln (kx) / ln (k)

86/443

8/19/2019 y = ln (kx) / ln (k)

87/443

8/19/2019 y = ln (kx) / ln (k)

88/443

8/19/2019 y = ln (kx) / ln (k)

89/443

8/19/2019 y = ln (kx) / ln (k)

90/443

8/19/2019 y = ln (kx) / ln (k)

91/443

8/19/2019 y = ln (kx) / ln (k)

92/443

8/19/2019 y = ln (kx) / ln (k)

93/443

8/19/2019 y = ln (kx) / ln (k)

94/443

100 120

n

8/19/2019 y = ln (kx) / ln (k)

95/443

8/19/2019 y = ln (kx) / ln (k)

96/443

8/19/2019 y = ln (kx) / ln (k)

97/443

8/19/2019 y = ln (kx) / ln (k)

98/443

8/19/2019 y = ln (kx) / ln (k)

99/443

8/19/2019 y = ln (kx) / ln (k)

100/443

8/19/2019 y = ln (kx) / ln (k)

101/443

8/19/2019 y = ln (kx) / ln (k)

102/443

8/19/2019 y = ln (kx) / ln (k)

103/443

8/19/2019 y = ln (kx) / ln (k)

104/443

8/19/2019 y = ln (kx) / ln (k)

105/443

8/19/2019 y = ln (kx) / ln (k)

106/443

8/19/2019 y = ln (kx) / ln (k)

107/443

8/19/2019 y = ln (kx) / ln (k)

108/443

8/19/2019 y = ln (kx) / ln (k)

109/443

8/19/2019 y = ln (kx) / ln (k)

110/443

8/19/2019 y = ln (kx) / ln (k)

111/443

8/19/2019 y = ln (kx) / ln (k)

112/443

8/19/2019 y = ln (kx) / ln (k)

113/443

8/19/2019 y = ln (kx) / ln (k)

114/443

8/19/2019 y = ln (kx) / ln (k)

115/443

8/19/2019 y = ln (kx) / ln (k)

116/443

8/19/2019 y = ln (kx) / ln (k)

117/443

8/19/2019 y = ln (kx) / ln (k)

118/443

8/19/2019 y = ln (kx) / ln (k)

119/443

8/19/2019 y = ln (kx) / ln (k)

120/443

8/19/2019 y = ln (kx) / ln (k)

121/443

 A^n = 2A

then n=ln2A / lnA

  2A lnA ln2A

1000 2000 6.907755279 7.6009024595

1010 2020 6.9177056098 7.6108527904

1020 2040 6.9275579063 7.6207050868

1030 2060 6.9373140812 7.6304612618

1040 2080 6.9469759921 7.6401231727

1050 2100 6.9565454432 7.6496926237

1060 2120 6.9660241871 7.6591713677

1070 2140 6.9754139275 7.668561108

1080 2160 6.9847163201 7.6778635007

1090 2180 6.9939329752 7.6870801558

1100 2200 7.0030654588 7.6962126393

1110 2220 7.0121152943 7.7052624749

1120 2240 7.0210839643 7.7142311448

1130 2260 7.0299729117 7.7231200923

1140 2280 7.0387835414 7.7319307219

1150 2300 7.0475172214 7.7406644019

1160 2320 7.0561752841 7.7493224647

1170 2340 7.0647590278 7.7579062084

1180 2360 7.0732697175 7.766416898

1190 2380 7.0817085861 7.7748557667

1200 2400 7.0900768358 7.7832240163

1210 2420 7.0983756386 7.7915228192

1220 2440 7.1066061377 7.7997533183

1230 2460 7.1147694484 7.8079166289

1240 2480 7.1228666586 7.8160138392

1250 2500 7.1308988303 7.8240460109

1260 2520 7.1388669999 7.8320141805

1270 2540 7.1467721795 7.839919361280 2560 7.1546153569 7.8477625375

1290 2580 7.1623974974 7.8555446779

1300 2600 7.1701195434 7.863266724

1310 2620 7.1777824162 7.8709295968

1320 2640 7.1853870156 7.8785341961

1330 2660 7.1929342212 7.8860814018

1340 2680 7.2004248929 7.8935720735

8/19/2019 y = ln (kx) / ln (k)

122/443

1350 2700 7.2078598714 7.901007052

1360 2720 7.2152399787 7.9083871593

1370 2740 7.2225660188 7.9157131994

1380 2760 7.2298387782 7.9229859587

1390 2780 7.2370590261 7.9302062067

1400 2800 7.2442275156 7.9373746962

1410 2820 7.2513449834 7.9444921639

1420 2840 7.2584121506 7.9515593312

1430 2860 7.2654297233 7.9585769038

1440 2880 7.2723983926 7.9655455731

1450 2900 7.2793188354 7.972466016

1460 2920 7.2861917147 7.9793388953

1470 2940 7.2930176798 7.9861648603

1480 2960 7.2997973668 7.9929445473

1490 2980 7.3065313989 7.9996785795

1500 3000 7.3132203871 8.0063675677

1510 3020 7.3198649298 8.0130121104

1520 3040 7.3264656138 8.0196127944

1530 3060 7.3330230144 8.0261701949

1540 3080 7.3395376954 8.032684876

1550 3100 7.3460102099 8.0391573905

1560 3120 7.3524411002 8.0455882808

1570 3140 7.3588308983 8.0519780789

1580 3160 7.365180126 8.0583273066

1590 3180 7.3714892952 8.0646364758

1600 3200 7.3777589082 8.0709060888

1610 3220 7.383989458 8.0771366385

1620 3240 7.3901814282 8.0833286088

1630 3260 7.3963352938 8.0894824744

1640 3280 7.4024515208 8.0955987014

1650 3300 7.4085305669 8.10167774751660 3320 7.4145728814 8.1077200619

1670 3340 7.4205789054 8.113726086

1680 3360 7.4265490724 8.119696253

1690 3380 7.4324838079 8.1256309885

1700 3400 7.43838353 8.1315307106

1710 3420 7.4442486495 8.1373958301

1720 3440 7.4500795698 8.1432267504

8/19/2019 y = ln (kx) / ln (k)

123/443

1730 3460 7.4558766875 8.1490238681

1740 3480 7.4616403922 8.1547875728

1750 3500 7.4673710669 8.1605182475

1760 3520 7.473069088 8.1662162686

1770 3540 7.4787348256 8.1718820061

1780 3560 7.4843686433 8.1775158238

1790 3580 7.4899708988 8.1831180794

1800 3600 7.4955419439 8.1886891244

1810 3620 7.5010821243 8.1942293048

1820 3640 7.5065917801 8.1997389606

1830 3660 7.5120712458 8.2052184264

1840 3680 7.5175208506 8.2106680312

1850 3700 7.5229409181 8.2160880986

1860 3720 7.5283317667 8.2214789473

1870 3740 7.5336937098 8.2268408904

1880 3760 7.5390270558 8.2321742364

1890 3780 7.5443321081 8.2374792886

1900 3800 7.5496091652 8.2427563457

1910 3820 7.554858521 8.2480057016

1920 3840 7.560080465 8.2532276456

1930 3860 7.5652752819 8.2584224625

1940 3880 7.5704432521 8.2635904326

1950 3900 7.5755846516 8.2687318321

1960 3920 7.5806997522 8.2738469328

1970 3940 7.5857888217 8.2789360023

1980 3960 7.5908521237 8.2839993042

1990 3980 7.5958899177 8.2890370983

2000 4000 7.6009024595 8.2940496401

2010 4020 7.6058900011 8.2990371816

2020 4040 7.6108527904 8.303999971

2030 4060 7.615791072 8.30893825262040 4080 7.6207050868 8.3138522674

2050 4100 7.6255950721 8.3187422527

2060 4120 7.6304612618 8.3236084423

2070 4140 7.6353038863 8.3284510668

2080 4160 7.6401231727 8.3332703533

2090 4180 7.644919345 8.3380665255

2100 4200 7.6496926237 8.3428398043

8/19/2019 y = ln (kx) / ln (k)

124/443

2110 4220 7.6544432265 8.347590407

2120 4240 7.6591713677 8.3523185482

2130 4260 7.6638772587 8.3570244393

2140 4280 7.668561108 8.3617082886

2150 4300 7.6732231211 8.3663703017

2160 4320 7.6778635007 8.3710106812

2170 4340 7.6824824465 8.3756296271

2180 4360 7.6870801558 8.3802273363

2190 4380 7.6916568228 8.3848040034

2200 4400 7.6962126393 8.3893598199

2210 4420 7.7007477945 8.3938949751

2220 4440 7.7052624749 8.3984096554

2230 4460 7.7097568645 8.402904045

2240 4480 7.7142311448 8.4073783254

2250 4500 7.7186854952 8.4118326758

2260 4520 7.7231200923 8.4162672728

2270 4540 7.7275351105 8.420682291

2280 4560 7.7319307219 8.4250779025

2290 4580 7.7363070965 8.4294542771

2300 4600 7.7406644019 8.4338115825

2310 4620 7.7450028035 8.4381499841

2320 4640 7.7493224647 8.4424696452

2330 4660 7.7536235466 8.4467707271

2340 4680 7.7579062084 8.4510533889

2350 4700 7.7621706071 8.4553177877

2360 4720 7.766416898 8.4595640786

2370 4740 7.7706452341 8.4637924147

2380 4760 7.7748557667 8.4680029472

2390 4780 7.7790486449 8.4721958255

2400 4800 7.7832240163 8.4763711969

2410 4820 7.7873820265 8.4805292072420 4840 7.7915228192 8.4846699997

2430 4860 7.7956465363 8.4887937169

2440 4880 7.7997533183 8.4929004988

2450 4900 7.8038433035 8.4969904841

2460 4920 7.8079166289 8.5010638095

2470 4940 7.8119734296 8.5051206102

2480 4960 7.8160138392 8.5091610197

8/19/2019 y = ln (kx) / ln (k)

125/443

2490 4980 7.8200379895 8.51318517

2500 5000 7.8240460109 8.5171931914

2510 5020 7.8280380321 8.5211852127

2520 5040 7.8320141805 8.5251613611

2530 5060 7.8359745817 8.5291217623

2540 5080 7.83991936 8.5330665406

2550 5100 7.8438486382 8.5369958187

2560 5120 7.8477625375 8.540909718

2570 5140 7.8516611779 8.5448083584

2580 5160 7.8555446779 8.5486918585

2590 5180 7.8594131547 8.5525603353

2600 5200 7.863266724 8.5564139046

2610 5220 7.8671055003 8.5602526809

2620 5240 7.8709295968 8.5640767773

2630 5260 7.8747391252 8.5678863057

2640 5280 7.8785341961 8.5716813767

2650 5300 7.882314919 8.5754620995

2660 5320 7.8860814018 8.5792285823

2670 5340 7.8898337514 8.582980932

2680 5360 7.8935720735 8.5867192541

2690 5380 7.8972964726 8.5904436532

2700 5400 7.901007052 8.5941542326

2710 5420 7.9047039139 8.5978510944

2720 5440 7.9083871593 8.6015343398

2730 5460 7.9120568882 8.6052040687

2740 5480 7.9157131994 8.6088603799

2750 5500 7.9193561907 8.6125033712

2760 5520 7.9229859587 8.6161331393

2770 5540 7.9266025992 8.6197497797

2780 5560 7.9302062067 8.6233533872

2790 5580 7.9337968748 8.62694405542800 5600 7.9373746962 8.6305218767

2810 5620 7.9409397623 8.6340869429

2820 5640 7.9444921639 8.6376393445

2830 5660 7.9480319906 8.6411791712

2840 5680 7.9515593312 8.6447065117

2850 5700 7.9550742733 8.6482214538

2860 5720 7.9585769038 8.6517240844

8/19/2019 y = ln (kx) / ln (k)

126/443

2870 5740 7.9620673088 8.6552144893

2880 5760 7.9655455731 8.6586927537

2890 5780 7.9690117811 8.6621589617

2900 5800 7.972466016 8.6656131965

2910 5820 7.9759083602 8.6690555407

2920 5840 7.9793388953 8.6724860758

2930 5860 7.982757702 8.6759048826

2940 5880 7.9861648603 8.6793120409

2950 5900 7.9895604493 8.6827076299