Question

Use the image to answer the question.

A U-shaped downward opening curve with 4 plotted points is on a coordinate plane. The x-axis ranges from negative 1 to 9 in increments of 1. The y-axis ranges from negative 10 to 100 in increments of 10.
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The curve begins at approximately left parenthesis negative 0.25 comma negative 10 right parenthesis. It passes through the plotted point left parenthesis 0 comma 0 right parenthesis then curves upward to pass through the plotted point left parenthesis 3 comma 90 right parenthesis. It peaks at approximately left parenthesis 4 comma 95 right parenthesis before descending to the plotted point left parenthesis 5 comma 90 right parenthesis. It curves downward to pass through the plotted point left parenthesis 8 comma 0 right parenthesis. The curve ends at approximately left parenthesis 8.25 comma negative 10 right parenthesis.

A quadratic function is graphed. Compare the estimated average rate of change for the quadratic function to the estimated average rate of change for the exponential function y=−6x
on the interval [0,5]
. Use one of the symbols <
, =
, or >
to describe the comparison.

(1 point)
The estimated average rate of change of the quadratic function
the estimated average rate of change of the exponential function.

Answer 1

The average rate of change for the quadratic on [0,5] is (90−0)/5 = 18.
For y = −6^x it is (−6^5 − (−6^0))/5 = (−7776 + 1)/5 = −1555.
18 > −1555, so use ">".