To estimate the amount of defoliation caused by the gypsy moth during a year, a forester

Chapter 5, Problem 109

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Forest Defoliation To estimate the amount of defoliation caused by the gypsy moth during a year, a forester counts the number of egg masses on \(\frac{1}{40}\) of an acre the preceding fall. The percent of defoliation y is approximated by

\(y=\frac{300}{3+17 e^{-0.0625 x}}\)

where x is the number of egg masses in thousands. (Source: USDA Forest Service)

(a) Use a graphing utility to graph the function.

(b) Estimate the percent of defoliation if 2000 egg masses are counted.

(c) Estimate the number of egg masses that existed if you observe that approximately \(\frac{2}{3}\) of a forest is defoliated.

(d) Use calculus to estimate the value of x for which y is increasing most rapidly.

Text Transcription:

1/40

y = 300/3 + 17e^-0.0625x

2/3