Question

Function f is an exponential function.

By what factor does the output value increase as each input value increases by 1?

Answer 1

If the input value increases by 1, the output value increases by 2.

Explanation:

The given table represents an exponential function, that means that variables show a sequence which have an increasing factor that we can find by division.

If we divide the second values by the first value, we could find the factor of the exponential function.

`(1)/(16)/ (1)/(64) =(1)/(16) * (64)/(1)=4`

So,
`f(x)` increases by a factor of 2.

Now, using the table we see that
`x` values increases by a difference of
`+2`, not a factor.

At the moment, while the input value increases by 2, the output value increases by 4.

This means that if the input value increases by 1, the output value increases by 2.

Therefore, the answer is 2.

Answer 2

Multiply the output value by 2 for each input value increases by 1

Explanation:

Function f is an exponential function

Since it is an exponential function , we find out common ratio of output first

WE divide second term by first term to get common ratio

`((1)/(16))/((1)/(64))`

`(1)/(16) * (64)/(1)= 4`

Change in output = 4

Now we find change in input

Input increases by 2 so change in input = 2

Factor that increase the output is
`(4)/(2) = 2`