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

Answer:

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

Step-by-step 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 $\frac{3}{16}\ to\ \frac{3}{4}$. Therefore, the factor by which the output changes is:

$r=\frac{\frac{3}{4}}{\frac{3}{16}} =\frac{3}{4}\times \frac{16}{3}=4$

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 $\frac{4}{2}=2$

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