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
[tex]f\left(x\right)=2^x+1[/tex]
Rebecca wants to find the average rate of change from x = -1 to x = 3.
so
at x₁ = -1
[tex]f\left(-1\right)\:=\:2^{-1}+1=\frac{1}{2}+1=\frac{3}{2}[/tex]
at x₂ = 3
[tex]f\left(3\right)\:=\:2^3+1=8+1=9[/tex]
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]
[tex]=\:\frac{\left[9\:-\:\frac{3}{2}\right]}{\left[3-\left(-1\right)\right]}[/tex]
[tex]=\frac{\frac{15}{2}}{4}[/tex]
[tex]=\frac{15}{8}[/tex]
Therefore, the average rate of change from x = -1 to x = 3 will be:
Average rate = 15/8
