Question

Use the image to answer the question.

A curve with 2 plotted points is on a coordinate plane. The x-axis ranges from negative 10 to 4 in increments of 1. The y-axis ranges from negative 4 to 18 in increments of 1.
▶Click for Long Desc

Compare the estimated average rates of change of the exponential function pictured above and the quadratic function f(x)=x2−20
over the interval [−9,2]
and identify which function has a greater rate of change than the other.

(1 point)

The estimated average rate of change of the exponential function over the interval [−9,2]
is negative, while the estimated average rate of change of f(x)
over the interval [−9,2]
is positive.

The estimated average rate of change of the exponential function over the interval [−9,2]
is greater than the magnitude of the estimated average rate of change of f(x)
over the interval [−9,2]
.

The estimated average rate of change of the exponential function over the interval [−9,2]
is less than the magnitude of the estimated average rate of change of f(x)
over the interval [−9,2]
.

The estimated average rate of change of both the exponential function and f(x)
over the interval [−9,2]
is approximately 1.5
.

Answer 1

Answer: The third choice.

Reason: For f(x)=x^2−20 the average rate over [−9,2] is (f(2)−f(−9))/(2−(−9)) = (4−20 − (81−20))/11 = (−16 − 61)/11 = −77/11 = −7, so its magnitude is 7. From the plot the exponential’s y-value only changes a small amount between x=−9 and x=2 (roughly from about 1 to a few units), so its average rate of change is much smaller than 7. Therefore the exponential’s average rate is less than the magnitude of f’s average rate.