Models of Exponent

ial and Log

Functions

Properties of

Logarithms

Solving Exponent

ial and Log

Functions

Exponential Growth

and Decay

100 100 100 100200 200 200 200300 300 300 300400 400 400 400500 500 500 500

100 Identify the model represented by

54

3)(

x

xf

100Exponential

Decay

200Identify the model represented by

a.

b.

xexf

231

1)(

xxf 5log2)(

200a.Logistics Growth

b. Logarithmic

300Identify the model

represented byxexf 567.0

2

1)(

300Exponential

Growth

400In 1985, you bought a sculpture for $380. Each year, t, the value, v, of the sculpture increases by 8%. Write an exponential model that describes this situation?

400 v=380(1.08)t

where t=0 represents 1985

500 Record albums

increased in popularity until about 1980. In 1980, 817 (million) record albums were sold. Each year after that, the number sold decreased by 27%. Write an exponential model which describes this situation.

500

y=817(0.73)x

where x =0 represents 1980

100Expand the following

logarithm

z

yx4

log

100

zyx log2

1loglog4

200

Use the change of base formula to solve the given

logarithm:3log7

200

5646.07log

3log

10

10

300Write the

expression as the logarithm of a

single quantity: zyx log3

1log5log2

300

3

52

logz

yx

400DAILY

DOUBLE!!!!

500Use the properties of

logarithms to expand the following logarithmic

expression)2(log 2 xx

500

)2log(2

1)log( xx

100Simplify the expression:

2

ln xe

100

2x

200Solve for x:

3log4 x

200

64x

300Solve the

exponential equation

algebraically:427 xe

300

4055.023ln x

400Solve the equation

algebraically:

2)1ln( 2 x

400

71828.11ex

500Solve for x:

)24ln()53ln()7ln( xxx

500

X = 7/3

100 Find the number of

years required for a $1000 investment to double at an 7% interest rate compounded continuously.

100

9.907.

2lnt

200Determine the amount of money that should be invested at a rate of 6% compounded

annually to produce a final balance of $2,000

in 5 years.

200$1,494.52

300An initial deposit of $2000 is made in a savings account for which the interest is

compounded continuously. The

balance will triple in 20 years. What is the annual rate of interest

for this account?

300

05.020

3lnr

400The number of bacteria N in a culture is given by the model below where t is the time in hours. If N = 280 when t = 10, estimate the

time required for the population to double in

size.

kteN 250

400

61.16 hours

500The population P of a city is given by P=2500ekt where t = 0 represents

1990. In 1945, the population was 1350.

Find the value of k.

500

0137.k

DAILY DOUBLE

Write the expression as the logarithm of a single quantity:

xxx ln3)1ln(2)1ln(2

1

DAILY DOUBLE

1)1(ln 3 xxx