Final answer:
The average rate of change of the function f(x) = et over the interval [-2, t] is (et - e^(-2t))/(t + 2)
Step-by-step explanation:
The average rate of change of a function over an interval is found by calculating the difference in the function values at the endpoints of the interval and dividing it by the difference in the x-coordinates of the endpoints. In this case, the function is f(x) = et, and the interval is [-2, t].
Let's calculate the average rate of change. At x = -2, the function value is f(-2) = e^(-2t). At x = t, the function value is f(t) = et. So the average rate of change is:
Average rate of change = (f(t) - f(-2)) / (t - (-2)) = (et - e^(-2t))/(t + 2)
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