Function f is an exponential function: x: 0, 1, 2, 3, 4
f(x): 1/4, 3/2, 9, 54, 324

What are the ratios of any 2 inputs that are 2 apart?

1/36

Step-by-step explanation:

I see that the functional values must be the product

3^a × 2^b

a starts at 0 (3⁰ = 1), and b starts at -2 (2^-2 = 1/4).

so, bringing x in this means

f(x) = 3^x × 2^(x-2)

0 and 2 are two apart.

so,

f(0)/f(2) = (3⁰×2^-2)/(3²×2⁰) = 1/4 / 9 = 1/36

f(1)/f(3) = 3/2 / 54 = 3/108 = 1/36

f(2)/f(4) = 9 / 324 = 1/36

...

i believe the correct answer is b.