C. f(x) = 8 (4)^x,
The explanation is shown in the images attached with the answer .
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
