Question

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 quadratic: (90 − 0)/(5 − 0) = 18.

For y = −6^x: y(0) = −1, y(5) = −7776, so average = (−7776 − (−1))/5 = −1555 (which is < 18).
(If the intended function was the linear y = −6x, its average rate is −6, still < 18.)

Therefore: 18 > (average rate of y = −6^x).

Use symbol: >