NAME ____________________________________________ DATE ____________________________ HOUR ______________

Chapter 7.4-7.8 Test Review

1. Graph y = −2(7)! 2. Graph y = (!!)!

2. y-intercept: ____________ domain: ______________ range: ________________

3. Determine the amount of an investment if $700 is invested at an interest rate of 8% compounded monthly for 9 years.

4. A new welding machine valued at $38,000 depreciates at a steady rate of 9% per year. What is the value of the welding machine in 10 years?

x y

x y

y-intercept: ____________ domain: ______________ range: ________________

5. Write an explicit equation for the nth term of the geometric sequence –3, 9, –27, … .

Find the first three terms of each sequence. 5. 𝑎! = 5, 𝑎! = 𝑎! ! ! – 3, n ≥ 2 6. 𝑎! = 3, 𝑎! = 2𝑎! ! ! + 4, n ≥ 2 Write a recursive formula for each sequence. 7. 18, 29, 40, 51, … 8. 2, –12, 72, –432, … 9. Find the first term of the geometric sequence with 𝑎! = 256 and 𝑎! = 1024.

10. Which is the equation for the nth term of the geometric sequence 6, 12, 24, ... ? F 𝑎! = 6 ⋅ 2! G 𝑎! = 2 ⋅ 3! H 𝑎! = 3 ⋅ 2! J 𝑎! = 3 ⋅ 2! ! ! 11. Which equation represents exponential decay? A y = 0.5𝑥! B y = 0.5𝑥! – x C y = 0.5(1 .07)! D y = 0.5(0.87)! 12. Which equation corresponds to the graph shown? F y = 3! + 2 H y = 2(3!) G y = 2(3! + 1) J y = (2 ⋅ 3)! + 1

13. A weight lifter can deadlift 275 pounds. She can increase the weight W(x) that she can lift according to the function W(x) = 275(1.05)!, where x represents the number of training cycles completed. How much will she deadlift after 5 training cycles?

14. A city’s population is about 763,000 and is increasing at an annual rate of 1.5%. Predict the population of the city in

50 years. 16. Find the third term of the sequence in which 𝑎! = –1 and 𝑎! = 5𝑎! ! ! – 3, if n ≥ 2.

___________ ___________

17. Find an explicit formula for 𝑎! = 10, 𝑎! = 𝑎! ! ! – 3, n ≥ 2. 18. Find a recursive formula for the arithmetic sequence 8, –2, –12, –22, ... . 19. Convert each explicit formula into a recursive formula and each recursive formula into an explicit formula.

a. 𝑎! = 7𝑛 − 1 c. 𝑎! 𝑎! = 𝑎!!! + 7, for 𝑛 ≥ 2

b. 𝑎! = 1 d. 𝑎! = −2 !!

!!!

𝑎! = 3𝑎!!!, for 𝑛 ≥ 2