Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Determine whether each table or rule represents an exponential function. Explain why or why not.

8. x	1	2	3	4
   y	2	8	32	128

9. x	0	1	2	3
   y	6	9	18	33

10. y = 4 · 5 x y equals 4 middle dot , 5 to the x
11. y = 12 · x 2 y equals 12 middle dot , x squared
12. y = − 5 · 0 . 25 x y equals negative 5 middle dot 0 . , 25 to the x
13. y = 7 x + 3 y equals 7 x plus 3

See Problem 2.

Evaluate each function for the given value.

14. f ( x ) = 6 x f open x close equals , 6 to the x  for x = 2 x equals 2
15. g ( t ) = 2 · 0 . 4 t g open t close equals 2 middle dot 0 . , 4 to the t  for t = − 2 t equals negative 2
16. y = 20 · 0 . 5 x y equals 20 middle dot 0 . , 5 to the x  for x = 3 x equals 3
17. h ( w ) = − 0.5 · 4 w h open w close equals negative 0.5 middle dot , 4 to the w  for w = 18 w equals 18
18. Finance An investment of $5000 doubles in value every decade. The function f ( x ) = 5000 · 2 x , f open x close equals , 5000 , middle dot , 2 to the x , comma  where x is the number of decades, models the growth of the value of the investment. How much is the investment worth after 30 yr?
19. Wildlife Management A population of 75 foxes in a wildlife preserve quadruples in size every 15 yr. The function y = 75 · 4 x , y equals 75 middle dot , 4 to the x , comma  where x is the number of 15-yr periods, models the population growth. How many foxes will there be after 45 yr?

See Problem 3.

Graph each exponential function.

20. y = 4 x y equals , 4 to the x
21. y = − 4 x y equals negative , 4 to the x
22. y = ( 1 3 ) x y equals . open , 1 third , close to the x
23. y = − ( 1 3 ) x y equals negative . open , 1 third , close to the x
24. y = 10 ⋅ ( 3 2 ) x y equals 10 dot . open , 3 halves , close to the x
25. y = 0.1 · 2 x y equals 0.1 middle dot , 2 to the x
26. y = 1 4 · 2 x y equals , 1 fourth , middle dot , 2 to the x
27. y = 1 . 25 x y equals 1 . , 25 to the x

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