Question

Which exponential function goes through the points (1, 8) and (4, 64)

Answer 1

(input, output)
f(x) = a*b^x

8 = 1*8^1
or
8 = 4*2^1
or
8 = 2*4^1

then looking at the second, 4 is the input x. there is only one option.

64 = 4*2^4
a = 4 , b = 2

f(x) = 4*2^x

Answer 2

The answer would be f(x)=4(2)x.
Hope this helps!