Question

The graph of f(x)=2^x+1 passes through the points (-1 , 1) and (3 , 16).

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

Rebecca's ERROR

Rebecca wrongly used the formula to calculate the average rate of change from x = -1 to x = 3.

She should have used the correct formula to calculate the average rate of change from x = -1 to x = 3 which is:

Average rate = [f(3) - f(-1)] / [3 - (-1)]

But, she reversed the formula.

The correct solution

Considering the graph

$f\left(x\right)=2^x+1$

Rebecca wants to find the average rate of change from x = -1 to x = 3.

so

at x₁ = -1

$f\left(-1\right)\:=\:2^{-1}+1=\frac{1}{2}+1=\frac{3}{2}$

at x₂ = 3

$f\left(3\right)\:=\:2^3+1=8+1=9$

Using the formula, we can determine the average rate of change from x = -1 to x = 3

Average rate = [f(3) - f(-1)] / [ x₂ - x₁]

                      $=\:\frac{\left[9\:-\:\frac{3}{2}\right]}{\left[3-\left(-1\right)\right]}$

                      $=\frac{\frac{15}{2}}{4}$

                      $=\frac{15}{8}$

Therefore, the average rate of change from x = -1 to x = 3 will be:

Average rate = 15/8