Question

The curve begins at approximately left parenthesis negative 3.5 comma 15 right parenthesis. It curves downward passing through the approximate points left parenthesis negative 3 comma 12 right parenthesis and left parenthesis negative 2 comma 6 right parenthesis to turn upward at left parenthesis 1.5 comma negative 2.5 right parenthesis. The curve passes through the plotted point left parenthesis 2 comma negative 2 right parenthesis then passes through the approximate points left parenthesis 4 comma 3 right parenthesis and left parenthesis 5 comma 8 right parenthesis before passing through the plotted point left parenthesis 6 comma 14 right parenthesis. The curve ends at approximately left parenthesis 6.2 comma 15 right parenthesis.

Compare the estimated average rate of change of the graphed quadratic function over the interval [2,6]
to the average rate of change of the exponential function y=34(2)x
over the same interval.

(1 point)

The estimated average rate of change of the exponential function is 0.16 greater than the estimated average rate of change of the quadratic function over the interval [2,6]
.

The estimated average rate of change of the exponential function is 7.25 greater than the estimated average rate of change of the quadratic function over the interval [2,6]
.

The estimated average rate of change of the quadratic function is 7.25 greater than the estimated average rate of change of the exponential function over the interval [2,6]
.

The estimated average rate of change of the quadratic function is 0.16 greater than the estimated average rate of change of the exponential function over the interval [2,6]
.
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Answer 1

Quadratic AROC on [2,6]: (14 − (−2)) / (6 − 2) = 16/4 = 4.

If y = (3/4)·2^x then y(2) = 0.75·4 = 3 and y(6) = 0.75·64 = 48, so exponential AROC = (48 − 3)/4 = 45/4 = 11.25.

11.25 − 4 = 7.25, so the estimated average rate of change of the exponential function is 7.25 greater than that of the quadratic.