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?




Enter your answer, as a simplified fraction, in the boxes.


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x −3 −2 −1 0 1 2 3

f(x) 8/27 8/9 8/3 8 2/4 7/2 2/16

Answer 1

27 9/16 21/16 1

Explanation:

The table with the input and output values for the exponential function is the following:

x −3 −2 −1 0 1 2 3

f(x) 8/27 8/9 8/3 8 2/4 7/2 2/16

Now we have to take three output values that are three values apart and calculate their ratio. Let's take x=0 and x=-3. The output ratio is:

`(f(0))/(f(-3))=(8)/(8/27)=27`

Let's now take x=1 and x=-2:

`(f(1))/(f(-2))=(2/4)/(8/9)=(2)/(4)\cdot (9)/(8)=(18)/(32)=(9)/(16)`

And so on:

`(f(2))/(f(-1))=(7/2)/(8/3)=(7)/(2)\cdot (3)/(8)=(21)/(16)`

`(f(3))/(f(0))=(2/16)/(8)=(2)/(16)\cdot 8=(2)/(2)=1`

So, the ratios are:

27 9/16 21/16 1