Calculus: Average rate of change An epidemiologist finds that the percentage N(t

Question

Calculus: Average rate of change An epidemiologist finds that the percentage N(t) of susceptible children who were infected on day t during the first three weeks of a measles outbreak is given, to a reasonable approximation, by the formula N(t) = 110t^2/(t^3 +5t^2-110t+380) a.) Draw the secant line whose slope is the average rate of change in infected children over the intervals [4,6] and [12,14] . Then compute these average rates (in units of percent per day). b.) Estimate the instantaneous rate of change in N(t) on day 12.

Explanation / Answer

N(t) = 110t^2/(t^3 +5t^2-110t+380)

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