Question

The Dapdap tree in the Philippines is prone to wasp infestation. Suppose that the percent P of defoliation is approximated by P= 300/3+17e^-0.0625xwhere x is the number of egg masses in thousands. If the percent of defoliation is 20%, approximately how many egg masses are there?

Answer 1

$P=20 \\ 20 = \frac{300}{3 +17e^{-0.0625x}} \\ 2 = \frac{30}{3 +17e^{-0.0625x}} \\ 15 = 3 +17e^{-0.0625x} \\ 17e^{-0.0625x} = 12 \\ e^{-0.0625x} = \frac{12}{17} \\ -0.0625x = ln(\frac{12}{17}) \\ x = \frac{-0.348306}{-0.0625} \\ x = 5.572 ≈ 6$