Sangeetha Pulapaka
0

STEP 1: Recall the laws of exponents

STEP 2: Recall what is an exponential function

https://mathinsight.org/exponential_function

STEP 3:  Write the rate of change

To see how a function changes over an interval, look at the endpoints.

The values of  f(x) =2^{x} at the endpoints x= 5 and x=8 are:

x(5) = 2^{5}

x(8) = 2^{8}

\frac{x(8)}{x(5)} = \frac{2^{8}}{2^{5}} = 2^{3} (using the quotient rule)

f(x) increases by a factor of 3 over the interval from x= 5 to x =8.

Skills to recall:

What is a factor

https://www.mathsisfun.com/definitions/factor.html