Question - Calculating Average Rate of Change for Exponential Function
Solution:
The question asks for the average rate of change of the function f(x) = 100 * 2^x on the interval [0,4].The average rate of change of a function over the interval [a, b] is given by the formula:\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]Here, our function f(x) = 100 * 2^x, our interval is [0, 4], so a = 0 and b = 4.We plug these into the function f to get f(0) and f(4):f(0) = 100 * 2^0 = 100 * 1 = 100f(4) = 100 * 2^4 = 100 * 16 = 1600Now plug f(0) and f(4) into the rate of change formula:\[ \text{Average Rate of Change} = \frac{f(4) - f(0)}{4 - 0} = \frac{1600 - 100}{4} = \frac{1500}{4} = 375 \]Hence, the average rate of change of f(x) on the interval [0,4] is 375.
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