An epidemiologist finds that the percentage N (t) of susceptible children who are sick

Chapter 2, Problem 26

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An epidemiologist finds that the percentage N (t) of susceptible children who are sick on day t during the first 3 weeks of a measles outbreak is given, to a reasonable approximation, by the formula (Figure 15) N (t) = 100t2 t3 + 5t2 100t + 380 Percent infected Time (days) 2 6 10 14 18 4 8 12 16 20 20 15 10 5 FIGURE 15 Graph of N. (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) Is the rate of decline greater at t = 8 or t = 16? (c) Estimate the rate of change of N (t) on day 12.