Question

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Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?

explain your answer step by step

Answer 1

Rate of change of the function: 60

Step-by-step explanation:

The exponential function in this problem is

$f(x)=2^{x+3}$

The rate of change of a function between a certain interval $x_1 \leq x \leq x_2$ is given by

$r=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

where

$f(x_1)$ is the value of the function calculated in $x_1$

$f(x_2)$ is the value of the function calculated in $x_2$

In this problem, the interval is

$1\leq x \leq 5$

So we have:

$f(x_1)=f(1)=2^{1+3}=2^4=16$

and

$f(x_2)=f(5)=2^{5+3}=256$

Therefore, the rate of change is:

$r=\frac{256-16}{5-1}=60$

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