exponential functions over unit intervals - How does f(x) change over from the interval x = 5 to x = 8?

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall the laws of exponents

STEP 2: Recall what is an 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