Chapter 5.4, Problem 10TE

Increasing Crop Yields If left untreated on bean stems, aphids (small insects that suck plant juices) will multiply at an increasing rate during the summer months and reduce productivity and crop yield of cultivated crops. But if the aphids are treated in mid-June, the numbers decrease sharply to fewer than 100/bean stem, allowing for steep rises in crop yield. The function

$f(t)=\{\begin{array}{l}62e^{1.152t}\text{ if }0\le t<1.5\\ 349e^{-1.324(t-1.5)}\text{ if }1.5\le t\le 3\end{array}$

gives the number of aphids after treatment on a typical bean stem at time t, where t is measured in months, with t = 0 corresponding to the beginning of May.

1. a. How many aphids are there on a typical bean stem at the beginning of June (t = 1)? At the beginning of July (t = 2)?
2. b. How fast is the population of aphids changing at the beginning of June? At the beginning of July?

Source: The Random House Encyclopedia.