Question

This table shows the input and output values for an exponential function f(x) .

What is the ratio of outputs for any two inputs that are three values apart?

x −3 −2 −1 0 1 2 3
f(x) 8/27 8/9 8/3 8 24 72 216


Enter your answer, as a simplified fraction

Answer 1

0.5

Explanation:

Answer 2

Given the table as shown below:

x y

-3 8/27

-2 8/9

-1 8/3

0 8

1 24

2 72

3 216

Taking any input variable x that are three apart:

i,e x = 0 and x = 3

The output values at x =0 and x = 3 are:

f(0) = 8 and f(3) = 216

Then;

The ratio of outputs is:

`(f(3))/(f(0)) = (216)/(8)= (27)/(1)` or 27 : 1

Therefore, the ratio outputs for any two inputs that are three values apart is:
`27: 1`