The graph of f(x)=2^x+1 passes through the points (-1 , 1) and (3 , 16). Rebecca wants to find the average rate of change from x = -1 to x = 3. Here is her work:

3− ( −1) / 16−1 = 4/15
a. Explain Rebecca's error. (2 points)

b. Find the correct average rate of change. (2 points)

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

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

so

at x₁ = -1

at x₂ = 3

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]

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

Average rate = 15/8

step-by-step explanation:

|ab| = 1.4 = 4

h = 1.4 = 4

a(abc) area = 4.4 = 16/2 = 8

area of abc = 8 cm^2

good luck ! ; )