Question

Function f is an exponential function.

x −4 −2 0 2 4
f(x) 3/16 3/4 3 12 48
By what factor does the output value increase as each input value increases by 1? Enter your answer in the box.

Answer 1

The output value increases by a factor of 2 as each input value increases by 1.

Explanation:

Given:

Function
`f(x)` is an exponential function.

The factor by which
`f(x)` increases with increase in
`x` is same as finding the ratio of two consecutive output values.

When
`x` increases from -4 to -2,
`f(x)` increases from
`(3)/(16)\ to\ (3)/(4)`. Therefore, the factor by which the output changes is:

`r=((3)/(4))/((3)/(16)) =(3)/(4)* (16)/(3)=4`

The increase in input value for increasing output value by a factor 4 is given as:

`\Delta x=-2-(-4)=-2+4=2`

So, with the increase of input value by 2, the output value increases by a factor of 4.

Therefore, with the increase of input value by 1, the output values increases by a factor
`(4)/(2)=2`

Thus, the output value increases by a factor of 2 as each input value increases by 1.