Question

To estimate the amount of defoliation caused by the gypsy moth during a year, a forester counts the number of egg masses on 1/40 of an acre the preceding fall. The percent defoliation y is approximated by the function below, where x is the number of egg masses in thousands.

y = 200 / 2 + 11e– ⁰.⁰⁶⁹⁵ˣ

(b) Estimate the percent of defoliation if 2000 egg masses are counted. (Round your answer to two decimal places.)
y = _____________ %

Answer 1

When estimating the percent of defoliation caused by gypsy moths for 2000 egg masses using the given function, the calculation yields approximately 17.29% defoliation.

Step-by-step explanation:

To estimate the percent of defoliation caused by the gypsy moth, we use the given function where x represents the number of egg masses in thousands. For 2000 egg masses, x would be 2 (since 2000 egg masses are 2 thousands). Plugging this into the function:

y = 200 / (2 + 11e–​0.0695×(2))

Performing the calculation using a calculator:

y = 200 / (2 + 11e–​0.139)

y = 200 / (2 + 11 × 0.86936)

y = 200 / (2 + 9.56296)

y = 200 / 11.56296

y ≈ 17.29%

Therefore, the estimated percent of defoliation if 2000 egg masses are counted is approximately 17.29%.