Find a and k and then evaluate the function Let f(x)=a(2 kx ) with f(0)=10 and f

Question

Find a and k and then evaluate the function

Let f(x)=a(2kx) with f(0)=10 and f(3)=640

Find f(2)

Please write neatly and explain as much as you can. Thank you.

Here is a photo from the book. Problem 35.

44. Start 34, f(x) = 3-2 grap a. sh 2. 1 + 2 In Exercises 35-38, find a and k and then evaluate the function. 35. Let f(x)-a(2kr) with f(0)-10 and f(3) 640. b. c Findf(2). Find f1). 37. Let/(x) = Find f(4). re 36. Let f(x) = 50-a (5kr) with f(0)-10 and f(2) 0. In Exer 45. In (x 4 with f(0) = 1 and 1 + ae kx 47. In 5 and f (4) = 4. 1 + ae-Tr with ./(0) Find f(10)

Explanation / Answer

f(x) = a(2^kx)

f(0) = 10

10 = a (2^0 )

a = 10

f(3) = 640

640 = a (2^3k)

640 = 10 (2^3k)

64 = 2^(3k)

ln 64 = 3k ln 2

k = 2

therefore , a = 10 , k = 2

function becomes

f(x) = 10 ( 2 ^2x)

f(2) = 10( 2^4)

f(2) = 160

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