Name __________________________________________________________________ Period ____________

Algebra 3-4 Unit 6 Part 1 Exponentials

6.1 I can write arithmetic sequences using recursive and explicit rules.

6.2 I can write geometric sequences using recursive and explicit rules.

6.3 I can find the sum of a geometric series.

6.4 I can graph exponential functions.

6.5-7 I can write and use exponential functions.

6.8-9 I can use compound interest formulas.

6.10-11

I can perform exponential regression.

My goal for this unit: _____________________________________________________ ______________________________________________________________________ What I need to do to reach my goal: ________________________________________ ______________________________________________________________________ ______________________________________________________________________

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.1 Arithmetic Sequences

An arithmetic sequence is a list of numbers (or terms) with a common difference between each

number.

0, 6, 12, 18, …

+6 +6 +6

The difference between terms is constant.

In this example, f(1) = 0, f(2) = 6, f(3) = 12, f(4) = 18, …. The common difference is 6.

Use the common difference d to write rules for an arithmetic sequence.

A recursive rule has this general form: f(1) = a and f(n) = f(n − 1) + d for n ≥ 2

First term = 0; difference = 6: f(1) = 0 and f(n) = f(n − 1) + 6 for n ≥ 2

An explicit rule has this general form: f(n) = f(1) + dn

Zero term = −6 and difference = 6: f(n) = −6 + 6n

Identify if the sequence is arithmetic. If it is, write the explicit and recursive rule.

1. −1, 2, −3, 4, …

2. 14, 12, 10, 8, … 3. 3, 6, 9, 27, …

4. −5, 0, 5, 10, …

5. 7, 4, 1, −2, … 6. 4, 7, 10, 13, …

7. 9, 23, 37, 51, …

8. 11, 13, 15, 17, … 9. 28, 22, 16, 10, …

Find how much you add or subtract

to move from term to term.

10.

11. 12.

13.

14. 15.

16. A recursive rule for an arithmetic sequence is

f(1) = 7, f(n) = f(n − 1) + 47 for n ≥ 2. Write an explicit rule for this sequence.

17. A recursive rule for an arithmetic sequence is

f(1) = −8, f(n) = f(n − 1) − 6.5 for n ≥ 2. Write an explicit rule for this sequence.

n 1 2 3 4 5

f(n) 8 12 16 20 24

n 1 2 3 4 5

f(n) 11 7 3 −1 −5

n 1 2 3 4 5

f(n) −20 −13 −6 1 8

n 1 2 3 4 5

f(n) 1 3 5 7 9

n 1 2 3 4 5

f(n) 15 13 11 9 7

n 1 2 3 4 5

f(n) 16 21 26 31 36

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.2 Geometric Sequences

A geometric sequence is a list of numbers (or terms) with a common ratio between each number.

Explicit Rule Recursive Rule

Example Write the explicit and

recursive rules for a geometric

sequence given the table of values.

Step 1: Find the common ratio, r, by dividing two

successive terms.

(2) 282

(1) 14

fr

f= = =

Step 2: Find the initial value, a, from the table. (0) 7a f= =

Step 3: Write the explicit rule by plugging in a and r. ( )= i( ) 7 2n

f n

Step 4: Write the recursive rule.

1.

n 0 1 2 3 4

f(n) 0.5 1.5 4.5 13.5 40.5

2.

n 0 1 2 3 4

f(n) 6 3 1.5 0.75 0.375

3.

n 0 1 2 3 4

f(n) 1

4 1 4 16 64

4.

5.

n 0 1 2 3 4

f(n) 162 18 2 2

9

2

81

6. 5, 10, 20, 40, 80, …

f(n) = Value of nth

Term

Value

of Previous Term

r = Common Ratio

f(n) = Value of nth

Term a = Initial Value

r = Common Ratio

n 0 1 2 3 4 …

f(n) 7 14 28 56 112 …

n 1 2 3 4 5

f(n) 2 6 18 54 162

f(n) = 2 f(n − 1); f(0) = 7

Write the explicit and recursive rules for each geometric sequence.

7. a1 = 9 and a2 = 18

8. a1 = 2 and a2 = 20 9. a1 = 5 and a3 = 80

Each rule represents a geometric sequence. If the given rule is recursive, write an explicit rule. If the rule is explicit, write a recursive rule. Assume that f(1) is the first term of the sequence.

10. f(1) = 7; f(n) = f(n − 1) i 3 for n ≥ 2

11. f(n) = 16(8)n−1

12. f(n) = 11(2)n−1

13. f(1) = 2.5; f(n) = f(n − 1) i 3.5 for n ≥ 2

14. f(1) = 27; f(n) = f(n − 1) i 1

3 for n ≥ 2

15. f(n) = −4(0.5)n−1

16. f(1) = 2

;3

f(n) = f(n − 1) i 8 for n ≥ 2

17. f(n) = −10(0.4)n−1

The population of a town is 20,000. It is expected to grow at 4% per year. 20. Write a recursive rule and an

explicit rule to predict the population, p(n), n years from today.

21. Use a rule to predict the population in 5 years and in 10 years.

22. Which rule is easier to use for Problem 21? Explain.

A bank account earns a constant rate of interest each month. The account was opened on March 1 with $18,000 in it. On April 1, the balance in the account was $18,045. 23. Write an explicit rule and a

recursive rule that can be used to find A(n), the balance after n months.

24. Find the balance after 5 months.

25. Find the balance after 5 years.

Name ____________________________________________________ Period __________________

Algebra 3-4 Unit 6.3 Arithmetic and Geometric Sequences

Identify each of the following as arithmetic, geometric, or neither.

1. 15, 11, 7, 3, …

2. 162, 54, 18, 6, … 3. 2, 5, 10, 17, …

4. 2, −8, 32, −128, …

5. 20, 27, 34, 41, … 6. 12, 6, 3, 1.5, …

7. 6, 10, 14, 18, …

8. 10, 20, 40, 80, … 9. 7, 2, −3, −8, …

10. f(n) = 5 + 3n

11. f(1) = 12; f(n) = 4 f(n − 1) 12. f(1) = 4; f(n) = f(n − 1) + 9

13. f(n) = 4(2)n 14. f(n) = −4n − 9

15. f(n) = −9(3)n

Calculate the sum of the finite geometric series.

16. 2, 12, 72, 432

17. −1, 5, −25, 125

18. 1, 2, 4, 8, …, 64

19. 3, −9, 27, −81, …, −729

20. 2, 6, 18, …, 162

21. 5, 15, 45, …, 1215

22. 5, −20, 80, …, −5120

23. 10, 60, 360, 2160, …, 77760

Write the recursive and explicit formula for each sequence.

24. 40, 43, 46, 49, 52, … Find the 80th term

25. −4, 12, −36, 108, −324, … Find the 8th term

26. −29, −34, −39, −44, −49, … Find the 75th term

27. 3, 6, 12, 24, … Find the 10th term

28. 1, 5, 25, 125, 625, … Find the 7th term

29. −30, −22, −14, −6, 2, …

Find the 100th term

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.4 Exponential Growth and Decay Functions

Use a graphing calculator to fill in the tables and graphs:

f(x) = 2x g(x) = 10x h(x) =

x

2

1 j(x) =

x

10

1

Describe/discuss what you notice about the first 2 graphs. (similarities/differences)

Describe/discuss what you notice about the last 2 graphs? (similarities/differences)

Which of the following would look like the first 2 graphs? Which would look like the last 2 graphs?

f(x) = 3x f(x) = 1.5x f(x) = x

5

1 f(x) =

x

3

5

Graph all of the following on one graph (different colors would help!) f(x) = 2x f(x) = 2x + 2

f(x) = 2x − 2 f(x) = 2x + 2

f(x) = 2x − 2

Graph all of the following on one graph (different colors would help!) f(x) = 2x

f(x) = 2(2x)

f(x) = )2(2

1 x

f(x) = −2(2x)

f(x) = )2(2

1 x−

Describe/discuss what each +2 or −2 does to the graph.

Describe/discuss what 2, 2

1, −2, and

2

1− each do to

the graph.

x f(x)

−3

−2

−1

0

1

2

3

x g(x)

−3

−2

−1

0

1

2

3

x h(x)

−3

−2

−1

0

1

2

3

x j(x)

−3

−2

−1

0

1

2

3

Directions: Sketch each parent and transformed graph. Describe the transformation.

1. y = (2)x y = 5(2)x

2. y = (3)x

y = −2(3)x

3. y = 2x

−= +

11(2) 3

2

xy

4. y = x

2

1

y = 32

1−

x

5. y = (0.5)x

y = −(0.5)x + 3 − 3 6. y = x

2

1

y =

x

2

13

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.5 Exponential Growth and Decay Functions

A historical car increases in value every year by 4%. In 2000 its value was $20,000. Fill in the table of values and graph.

Year t = 0 Calculation Car Value

2000 0 20,000 20,000 2001 1 20,000(1.04)

2002 20,000(1.04)(1.04) 2003

2004 2005 2025

t What do you do to each car value to get the next year’s car value? ______________________________________________________ A car decreases in value every year by 4%. In 2000 its value was $20,000. Fill in the table of values and graph.

Year t = 0 Calculation Car Value

2000 0 20,000 20,000 2001 1 20,000(0.96)

2002 20,000(0.96)(0.96) 2003

2004 2005

2025 t

Where did (0.96) come from? ______________________________________________________

Directions: Write an exponential equation, then use it to find the value after the given amount of time.

1. Annual sales for a store are $270,000 and are increasing at a rate of 7% per year; 3 years

2. The population of a school is 800 and is decreasing at a rate of 2% per year; 4 years

3. The bird population in a forest is about 2300 and is decreasing at a rate of 4% per year; 10 years

4. The population of a school is 2200 and is increasing at a rate of 2%; 6 years

5. Cost of a piece of technology is $280 and is decreasing a rate of 12% per year; 5 years

6. The value of a vase is $200 and is increasing at a rate of 8%; 12 years

7. A rare guitar worth $12,000 that is expected to increase in value by 12% per year; 5 years

8. A truck worth $28,000 decreases 9.5% each year; 8 years

9. Value of a home worth $180,000 increases by 3% each year; 20 years

10. Value of a computer is $800 which decreases by 12% every month; 2 years

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.6 Exponential Growth and Decay Functions

Directions: Solve each problem showing all work.

1. An exponential function f(x) passes through the points (2, 360) and (3, 216). Write an equation for f(x). Use your equation to find the value when x = 9.

2. If a basketball is bounced from a height of 15 feet, the function f(x) = 15(0.75)x gives the height of the ball in feet of each bounce, where x is the bounce number. What will be the height of the 5th bounce? Round to the nearest tenth of a foot.

What does the (0.75) represent in terms of the problem? Is this growth or decay? What is the growth/decay rate?

3. The annual sales for a fast food restaurant are $650,000 and are increasing at a rate of 4% per year. Write the function f(n) that expresses the annual sales after n years. Find the annual sales after 5 years. When will the annual sales be $800,000?

4. The value of a company’s equipment is $25,000 and decreases at a rate of 15% per year. Write the function, f(n), that expresses the value of the equipment after n years. Find the value of the equipment in year eight. When will the equipment’s value be $10,000?

5. In 1995, the population of a town was 33,500. It is decreasing at a rate of 2.5% per decade. Write the function, f(n), that expresses the population of the town after n decades. What is the expected population of the town in the year 2025 to the nearest hundred? When will the population be 20,000 people?

6. Starting with 25 members, a club doubled its membership every year. Write the function f(n) that expresses the number of members in the club after n years. Find the number of members after 6 years. When will the club have 500 members?

7. During a certain period of time, about 70 northern sea otters had an annual growth rate of 18%. Write the function f(n) that expresses the population of sea otters after n years. Then find the population of sea otters after 4 years. When will the population be 200?

8. Odette has two investments that she purchased at the same time.

Investment 1: $10,000; earns 4% interest each year. Investment 2: $8,000; earns 6% interest each year. Write exponential functions for each investment

I1(t) = I2(t) =

What is each investment’s value after 5 years?

I1(5) = I2(5) =

Which is a better investment? Explain.

9. A town was founded with a population of 3000. The population then doubled every decade. Write the function, p(n), that expresses the town’s population after n decades. Find the population four decades after its founding. When will the population reach 20,000?

10. In 2011, a small town had a population of 15,000. The population has been decreasing by 3% every year. Write the function, p(n), that expresses the town’s population after n years.

What is the expected population in the year 2015 to the nearest hundred? When will the population reach 5,000?

11. The half-life of a radioactive substance is the average amount of time it takes for half of its atoms to decay. Suppose you started with 200 grams of a substance with a half-life of 3 minutes. How many minutes have passed if 25 grams now remain? Explain your reasoning.

12. Colleen’s office equipment is depreciating at a rate of 9% per year. She paid $24,500 for it in 2009. Write the function f(n) that expresses the value of the equipment after n years. What will the equipment be worth in 2015 to the nearest hundred dollars? Once the equipment reaches a value of $5,000 she will need to replace it all. When will this happen?

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.7 Exponential Growth and Decay Functions

Directions: Solve each problem showing all work.

1. A car depreciates in value by 20% each year. Graham argued that the value of the car after 5 years must be

$0, since 20% i 5 = 100%. Do you agree or disagree? Explain fully.

2. A stock opens with a price of $0.59. Over the first three days, the value of the stock increases on average by 50% per day. If this trend continues, how many days will it take the stock to be worth $6?

3. A quantity of insulin used to regular sugar in the bloodstream breaks down by about 5% each minute after the injection. A bodyweight-adjusted dose is generally 10 units. How long does it take for the remaining insulin to be half of the original injection?

4. A lamp is appraised for $1000. The appraiser states that the values is appreciating by 8% per year. In how many years will the value be $2000?

5. Guitars create a note when a string vibrates back and forth. The distance the middle string moves from the center is called the amplitude which starts at 0.75 mm when a note is first struck. Amplitude decays at a rate of 25% per second. Calculate the time it takes for an amplitude of 0.75 mm to reach 0.1 mm.

6. You buy a video game console for $500 and sell it 5 years later for $100. The resale value decays exponentially over time. Write a function that represents the resale value.

7. Bill invests $3000 in a bond fund with an interest rate of 9% per year. If Bill does not withdraw any of the money, in how many years will it be worth $5000?

8. The estimated value of a 1948 Tucker 48 automobile in excellent condition has risen at an approximately exponential rate from about $500,000 in December 2006 to about $1,400,000 in December 2013. Find an equation for the value of the car over time.

What is the growth rate? If the trend continues, what will the car be worth

in December of 2019?

9. The estimated value of a ring was $4,000 in 2011. In 2017 it was estimated to have a value of $2,500. Find an equation for the value of the ring over time.

What is the decay rate? If the trend continues, when will the ring be

worth $1000?

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.8 Compound Interest

Al puts $1000 in a conventional bond that pays 4% simple interest per year but only on the initial investment.

Year Interest Earned End Value 0 0 1000

1 1000 × 0.04 = 40 1040

2 1000 × 0.04 = 40 1080

3 4 5

Ben puts $1000 in a zero-coupon bond that pays 4% compound interest compounded yearly.

Year Interest Earned End Value 0 0 1000.00

1 1000 × 0.04 = 40 1040.00

2 1040 × 0.04 = 41.60 1081.60

3 4 5

Charlie puts $1000 in a savings account that pays 4% compound interest compounded monthly.

Year tn

n

rPtV

•

+= 1)(

End Value

0

0 1000.00

1 112

12

04.011000

•

+

1040.74

2 212

12

04.011000

•

+

1083.14

3

4

5

Dan puts $1000 in a savings account that pays 4% compound interest compounded daily.

Year tn

n

rPtV

•

+= 1)(

End Value

0

0 1000.00

1 1365

365

04.011000

•

+

1040.81

2 2365

365

04.011000

•

+

1083.28

3

4

5

Ed puts $1000 in a savings account that pays 4% compound interest compounded continuously.

Year trPetV •=)( End Value

0 0 1000.00

1

1000e0.04• 1 1040.81

2

1000e0.04 • 2 1083.29

3

4

5

Explain the difference between simple and compound interest and compounding continuously. __________________________________________ __________________________________________ Which would you want to be used for your money? __________________________________________

Directions: Read each problem and solve showing all work. Write the equation you typed into the calculator.

1. Shiloh plans to deposit money into one of the following accounts. Which should he choose?

• 4.25% compounded monthly

• 4.8% compounded semiannually

2. Yolanda plans to deposit money into one of the following accounts. Which should she choose?

• 8.25% compounded continuously

• 8.16% compounded monthly

3. Tom plans to deposit money into one of the following accounts. Which should he choose?

• 6% compounded quarterly

• 5.5% compounded monthly

4. You invest $800 in an account that pays 3.25% interest compounded monthly. How much will the account be worth in 8 years?

5. You invest $900 in an account that pays 1.8% interest compounded daily. How much will you have in your account in 12 years?

6. You borrow $12,000 for a car at an interest rate of 5% compounded monthly. If you pay back the loan after 6 years, how much will you have paid for the car?

7. You buy clothes for $180 and put the purchase on a credit card that charges interest of 18% compounded monthly. If you pay off your credit card in 6 months, how much would the clothes cost you?

8. You borrow $2,000 from your friend who is going to charge you 3% interest compounded daily. If you pay your friend back after 2 years, how much will you owe?

9. You borrow $160,000 for a house paying interest rate of 3.625% compounded monthly. How much do you end up paying for the house if it takes you 30 years to pay it off?

10. Bacteria grows exponentially at a rate of 12% per year compounded continuously. If there are 5000 cells to begin, how many will there be in 2 years?

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.9 Compound Interest

Directions: Read each problem and solve showing all work. Write the equation you typed into the calculator.

1. The principal amount, $6250, earns 4.25% interest compounded annually. How long will it take for the account’s value to surpass $9500?

2. The principal amount, $4200, earns 3.6% interest compounded quarterly. How long will it take for the account’s value to surpass $15,000?

3. The principal amount, $13,000, earns 8.7% interest compounded continuously. How long will it take for the account’s value to reach $80,000?

4. The principal amount, $16,550, earns 2.89% interest compounded annually. How long will it take for the account’s value to surpass $75,250?

5. The principal amount, $25,700, earns 6.925% interest compounded semiannually. How long will it take for the account’s value to surpass $150,000?

6. The principal amount, $123,500, earns 7.65% interest compounded continuously. How long will it take for the account’s value to reach $300,000?

7. The principal amount, $500, earns 4% interest compounded annually. How long will it take for the account’s value to surpass $1000?

8. The principal amount, $500, earns 4% interest compounded monthly. How long will it take for the account’s value to surpass $1000?

9. The number of animals, 500, increases exponentially at a rate of 14% compounded continuously. How long will it take the population of animals to reach 1000?

10. Fatima opens an account with $1300 that earns 3.5% interest, compounded monthly. How long will it take the account value to be $2500?

11. Eli opens an account with $10,000 that earns 6% interest, compounded continuously. How long will it take the account value to be $20,000?

12. Jerry opens an account with $15,000 that earns 3.25% interest, compounded monthly. How long will it take the account value to be $30,000?

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.10 Regression

You have done linear and other regressions using technology in this and prior math classes. Use technology to perform exponential regression to find the function that best models the given data. Round each value to the hundredth.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

x 1 2 3 4 5

f (x) 14 7.1 3.4 1.8 0.8

x 2 12 22 32 42

f (x) 5 20 80 320 1280

x 2 4 6 8 10

f (x) 413.2 45.5 4.9 0.6 0.1

x 1 2 3 4 5

f (x) 11.3 8.4 6.3 4.7 3.6

x 2 4 6 8 10

f (x) 14.2 21.3 33.9 57.2 99.8

x −1 0 1 2 3

f (x) 48 24 12 6 3

x 1 2 3 4 5

f (x) 9.3 21.8 50.8 118.6 276.6

x 0 1 2 3 4

f (x) 1.2 1.6 2.0 2.6 3.4

x 0 1 2 3 4

f (x) 56 50.4 45.4 40.8 36.7

x 0 1 2 3 4

f (x) 20 22 24 27 29

11. Bernice is selling seashells she has found at the beach. The price of each shell depends on its length. Find an exponential model for the data.

What is the length of a shell selling for $9.00? If Bernice found a 40 cm conch shell, how much could she sell it for?

Length of Shell (cm) 5 8 12 20 25

Price ($) 2 3.5 5 18 40

12. Use exponential regression to find a function that models this data.

When will the population exceed 50,000? What will the population be after 100 years?

Time (years) 0 10 20 30 40

Population (thousands) 10.1 9.8 17.5 19.9 28.7

13. Use exponential regression to find a function that models this data.

Time (min) 1 3 6 8 10

Bacteria 413 575 945 1316 1832

When will the number of bacteria reach 2500? How many bacteria will exist after 1 hour?

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.11 Regression

The table below shows the total attendance at major league baseball games, at 10-year intervals since 1930. Use the table for the problems that follow. Round all answers to the nearest thousandth.

Major League Baseball Attendance (y), in millions, in years since 1930 (x)

x 0 10 20 30 40 50 60 70 80

y 10.1 9.8 17.5 19.9 28.7 43.0 54.8 72.6 73.1

1. Use a graphing calculator to find a linear regression equation for this data. ______________________________________________________ 2. Graph the linear model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 3. Use a graphing calculator to find a quadratic regression equation for this data. ______________________________________________________ 4. Graph the quadratic model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 5. Use a graphing calculator to find an exponential regression equation for this data. ______________________________________________________ 6. Graph the exponential model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 7. Use the exponential regression equation to predict major league baseball attendance in 2020. Based on the

pattern of data, do you think this is a reasonable prediction? Explain. A pot of boiling water is allowed to cool for 50 minutes. The table below shows the temperature of the water as it cools. Use the table for the problems that follow. Round all answers to the nearest thousandth.

Temperature of Water (y), in degrees Celsius, after cooling for x minutes

x 0 5 10 15 20 25 30 35 40 45 50

y 100 75 57 44 34 26 21 17 14 11 10

1. Use a graphing calculator to find a linear regression equation for this data. ______________________________________________________ 2. Graph the linear model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 3. Use a graphing calculator to find a quadratic regression equation for this data. ______________________________________________________ 4. Graph the quadratic model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 5. Use a graphing calculator to find an exponential regression equation for this data. ______________________________________________________ 6. Graph the exponential model along with the data. Does it seem like the model is a good fit for the data? ______________________________________________________ 7. Use each regression model to estimate the temperature of the water after 55 minutes. Which estimation

seems the most likely? ______________________________________________________________________________

Name ____________________________________________________________ Period __________________

Algebra 3-4 Unit 6.12 Are You Ready for Unit 6 Part 1 Assessment

I can use arithmetic and geometric sequences. 1. Write the explicit rule for an arithmetic sequence

given by the recursive rule f(n) = f(n − 1) + 5,

n ≥ 0, f(0) = −9.

2. Write the explicit rule for an arithmetic sequence

given by the recursive rule f(n) = f(n − 1) − 3,

n ≥ 0, f(1) = 25.

3. Write the explicit rule for an arithmetic sequence

given by the recursive rule f(n) = f(n − 1) + 8,

n ≥ 0, f(0) = 40.

4. Given the geometric sequence shown: What is the common ratio, r ? Find f(1). What is the explicit rule? What is the recursive rule?

5. Given the geometric sequence shown: What is the common ratio, r ? Find f(1). What is the explicit rule? What is the recursive rule?

6. Given the geometric sequence shown: What is the common ratio, r ? Find f(1). What is the explicit rule? What is the recursive rule?

7. Given the following series

7 − 21 + 63 − … + 567

Find the first term, a ________ Find the common ratio, r ________ Find the number of terms, n ________ Calculate the sum of the series using the formula.

8. Given the following series 12 + 24 + 48 + … + 1536

Find the first term, a ________ Find the common ratio, r ________ Find the number of terms, n ________ Calculate the sum of the series using the formula

n 0 1 2 3 …

( )f n 576 432 324 243 …

n 0 1 2 3 …

( )f n 1215 405 135 45 …

n 0 1 2 3 …

( )f n 1728 1152 768 512 …

9. Find the explicit rule for the following sequence.

17, 68, 272, 1088, …

Use your rule to determine the 9th term of the sequence.

10. Find the explicit rule for the following sequence.

−27, 81, −243, 729, …

Use your rule to determine the 8th term of the sequence.

I can graph and use exponential functions. 11. The value of a car is decreasing at a rate of 12%

per year. It was new in 2010 and had a value of $25,000.

Is this growth or decay? In what year will the car have a value of $5,000? What is the car’s predicted value in the year 2024?

12. The population of a city is increasing at a rate of 7% per year since a business opened their headquarters in that city in the year 2012. In 2012 the population was 22,000.

Is this growth or decay? What is the predicted population of the city in 2030? In what year will the population be about 30,000?

13. You are planning to invest $2,000 in one of the following accounts for 5 years. Calculate each ending value and determine which the best choice is.

Rate 2.4% compounded yearly

2.35% compounded monthly

2.3% compounded daily

2.25% compounded continuously

Value after 5 years

Best choice: ________________________________________________________________

14. You are planning to invest $5,000 in one of the following accounts for 5 years. Calculate each ending value and determine which the best choice is.

Rate 1.25% compounded yearly

1.22% compounded monthly

1.21% compounded daily

1.2% compounded continuously

Value after 5 years

Best choice: ________________________________________________________________

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