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
A. 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]
B. 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]
C. 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] .
D.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] .
To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints and divide by the difference in the inputs.
For the quadratic function, let's find the average rate of change over the interval [2,6].
The value of the function at x=2 is f(2) = 3, and at x=6 is f(6) = 15.
So, the change in function values is 15-3 = 12.
The difference in inputs is 6-2 = 4.
Therefore, the average rate of change of the quadratic function over the interval [2,6] is 12/4 = 3.
For the exponential function y=34(2)^x, let's find the average rate of change over the same interval.
The value of the function at x=2 is 34(2)^2 = 34(4) = 136, and at x=6 is 34(2)^6 = 34(64) = 2176.
So, the change in function values is 2176-136 = 2040.
The difference in inputs is 6-2 = 4.
Therefore, the average rate of change of the exponential function over the interval [2,6] is 2040/4 = 510.
Comparing the two average rates of change, we can see that the average rate of change of the exponential function (510) is greater than the average rate of change of the quadratic function (3).
Therefore, the correct response is:
B. 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].