A B C The fraction of a city\'s population infected by a flu virus is plotted as

Question

A B C The fraction of a city's population infected by a flu virus is plotted as a function of time (in weeks). (This is represented with the curved graph.) (a) First estimate the slopes of lines A and B. (Include units.) What quantity is represented by the slope of line A? What quantity is represented by the slope of line B? (b) Is the flu spreading more rapidly at t = 1, 2, or 3 weeks? Explain your reasoning. (c) Explain what is happening to the spread of the flu between the 4^th and 6^th weeks.

Explanation / Answer

(a) Slope A is the average rate of change over the interval [4, 6], whereas slope B is the
instantaneous rate of change at t = 6.
Slope A (.28 .19)/2 = .045, whereas slope

B (.28 .15)/6 = .0217.
(c) Among times t = 4, 5, 6, the flu is spreading most rapidly at t = 4 since the slope is
greatest at that instant.
(b) Among times t = 1, 2, 3, the flu is spreading most rapidly at t = 3 since the slope is
greatest at that instant.

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