Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Identify the initial amount a and the growth factor b in each exponential function.

9. g ( x ) = 14 · 2 x g open x close equals 14 middle dot , 2 to the x
10. y = 150 · 1 . 0894 x y equals 150 middle dot 1 . , 0894 to the x
11. y = 25 , 600 · 1 . 01 x y equals 25 comma 600 middle dot 1 . , 01 to the x
12. f ( t ) = 1 . 4 t f open t close equals 1 . , 4 to the t

13. College Enrollment The number of students enrolled at a college is 15,000 and grows 4% each year.

    1. The initial amount a is   . begin box , , end box .
    2. The percent rate of change is 4%, so the growth factor b is 1 +   =   . 1 plus begin box , , end box equals begin box , , end box .
    3. To find the number of students enrolled after one year, you calculate 15 , 000 ·   . 15 comma 000 middle dot begin box , , end box .
    4. Complete the equation y =   ·     y equals begin box , , end box middle dot , begin box , , end box super begin box , , end box end super  to find the number of students enrolled after x years.
    5. Use your equation to predict the number of students enrolled after 25 yr.
14. Ecology A town has 10 acres of conservation land. The town plans to increase the amount of conservation land about 5% every 10 yr. If the town continues to follow their plan, how much conservation land will there be after 50 yr?

See Problem 2.

Find the balance in each account after the given period.

15. $4000 principal earning 6% compounded annually, after 5 yr
16. $12,000 principal earning 4.8% compounded annually, after 7 yr
17. $500 principal earning 4% compounded quarterly, after 6 yr
18. $20,000 deposit earning 3.5% compounded monthly, after 10 yr
19. $5000 deposit earning 1.5% compounded quarterly, after 3 yr
20. $13,500 deposit earning 3.3% compounded monthly, after 1 yr
21. $775 deposit earning 4.25% compounded annually, after 12 yr
22. $3500 deposit earning 6.75% compounded monthly, after 6 months

See Problem 3.

Identify the initial amount a and the decay factor b in each exponential function.

23. y = 5 · 0 . 5 x y equals 5 middle dot 0 . , 5 to the x
24. f ( x ) = 10 · 0 . 1 x f open x close equals 10 middle dot 0 . , 1 to the x
25. g ( x ) = 100 ( 2 3 ) x g , open x close , equals 100 . open , 2 thirds , close to the x
26. y = 0.1 · 0 . 9 x y equals 0.1 middle dot 0 . , 9 to the x
27. Population The population of a city is 45,000 and decreases 2% each year. If the trend continues, what will the population be after 15 yr?

B Apply

State whether the equation represents exponential growth, exponential decay, or neither.

28. y = 0.93 · 2 x y equals , 0.93 , middle dot , 2 to the x
29. y = 2 · 0 . 68 x y equals 2 middle dot 0 . , 68 to the x
30. y = 68 · x 2 y equals 68 middle dot , x squared
31. y = 68 · 0 . 2 x y equals 68 middle dot 0 . , 2 to the x

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