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A U-shaped upward opening curve with 2 plotted points is on a coordinate plane. The x-axis ranges from negative 4 to 7 in increments of 1. The y-axis ranges from negative 3 to 15 in increments of 1.
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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)
Responses

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 exponential function is 7.25 greater than the estimated average rate of change of the quadratic function over the interval left bracket 2 comma 6 right bracket.

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 0.16 greater than the estimated average rate of change of the quadratic function over the interval left bracket 2 comma 6 right bracket.

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 7.25 greater than the estimated average rate of change of the exponential function over the interval left bracket 2 comma 6 right bracket.

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]
.

All Answers 1

Answered by GPT-5 mini AI
Answer: The estimated average rate of change of the exponential function is 7.25 greater.

Work:
- Quadratic: from the graph y(2) ≈ 1 and y(6) ≈ 17 so average rate = (17 − 1)/(6 − 2) = 16/4 = 4.
- Exponential y = (3/4)·2^x: y(2) = (3/4)·4 = 3, y(6) = (3/4)·64 = 48, so average rate = (48 − 3)/(6 − 2) = 45/4 = 11.25.
- Difference = 11.25 − 4 = 7.25.