Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Graph each function.

10. y = 6 x y equals , 6 to the x
11. y = 3 ( 10 ) x y equals 3 . open 10 close to the x
12. y = 1000 ( 2 ) x y equals , 1000 . open 2 close to the x
13. y = 9 ( 3 ) x y equals 9 . open 3 close to the x
14. f ( x ) = 2 ( 3 ) x f open x close equals 2 . open 3 close to the x
15. s ( t ) = 1 . 5 t s open t close equals 1 . , 5 to the t
16. y = 8 ( 5 ) x y equals 8 . open 5 close to the x
17. y = 2 2 x y equals , 2 super 2 x end super

See Problem 2.

Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the y-intercept.

18. y = 129 ( 1.63 ) x y equals 129 . open , 1.63 , close to the x
19. f ( x ) = 2 ( 0.65 ) x f open x close equals 2 . open , 0.65 , close to the x
20. y = 12 ( 17 10 ) x y equals 12 . open , 17 over 10 , close to the x
21. y = 0.8 ( 1 8 ) x y equals 0.8 . open , 1 eighth , close to the x
22. f ( x ) = 4 ( 5 6 ) x f open x close equals 4 . open , 5 sixths , close to the x
23. y = 0.45 ( 3 ) x y equals , 0.45 . open 3 close to the x
24. y = 1 100 ( 4 3 ) x y equals , 1 100th . open , 4 thirds , close to the x
25. f ( x ) = 2 − x f open x close equals , 2 super negative x end super

See Problems 3 and 4.

26. Interest Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 4%. If no money is added or withdrawn from the account, answer the following questions.

    1. How much will be in the account after 3 years?
    2. How much will be in the account after 18 years?
    3. How many years will it take for the account to contain $2500?
    4. How many years will it take for the account to contain $3000?

See Problem 5.

Write an exponential function to model each situation. Find each amount after the specified time.

27. A population of 120,000 grows 1.2% per year for 15 years.
28. A population of 1,860,000 decreases 1.5% each year for 12 years.
29. 1. Sports Before a basketball game, a referee noticed that the ball seemed under-inflated. She dropped it from 6 feet and measured the first bounce as 36 inches and the second bounce as 18 inches. Write an exponential function to model the height of the ball.
    2. How high was the ball on its fifth bounce?

Table of Contents