Question

Which exponential function goes through the points (1, 32) and (4, 2048)?

A. f(x) = 4(4)x

B. f(x) = 8(2)-x

C. f(x) = 8(4)x

D. f(x) = 4(4)-x

Answer 1

C. f(x) = 8 (4)^x,

The explanation is shown in the images attached with the answer .

Answer 2

Answer: f(x) = 4*(4)ˣ Option C

Explanation:

We know the standard function of exponential function :

f(x) = a*bˣ

where is initial value

b is growth factor

x is time

Now given that two coordinates (1,32) & (4,2048)

Now put x = 1, f(x) = 32

32 = a*b¹

a*b = 32 ----------------------- (1)

now use second point

2048 = a * b⁴

a*b⁴ = 2048 ----------------------(2)

Now divide (2) / (1)

b³ = 64

b = 4

Put b = 4 in equation (1)

a (4) = 32

a = 8

So, final function is :

f(x) = 8*(4)ˣ