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=3/4(2)x over the same interval.
A) 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]
B) 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]
C) 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]
D) 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]
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To find the estimated average rate of change of the quadratic function over the interval [2,6], we need to find the difference in y-values divided by the difference in x-values.
For the quadratic function, let's take x = 2 and x = 6:
y(2) = -5, y(6) = 15
The average rate of change of the quadratic function is:
(15 - (-5))/(6 - 2) = 20/4 = 5
Now let's find the average rate of change of the exponential function y=3/4(2)^x over the same interval [2,6]. We need to find the difference in y-values divided by the difference in x-values.
For the exponential function, let's take x = 2 and x = 6:
y(2) = 3/4(2)^2 = 3, y(6) = 3/4(2)^6 = 24
The average rate of change of the exponential function is:
(24 - 3)/(6 - 2) = 21/4 = 5.25
Comparing the two average rates of change, we see that the average rate of change of the exponential function is 0.25 greater than the average rate of change of the quadratic function.
Therefore, the answer is:
B) 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].