calculus problem

Question

In desert areas of the western United States, lizards and other reptiles are harvested for sale as pets. Because reptiles hibernate during the winter months, no reptiles are gathered during the months of January, February, November, and December. The number of lizards harvested during the remaining months can be modeled as

h(m) = 15.3 sin(0.805m + 2.95) + 16.7

where m is the month of the year (i.e., m = 3

represents March), 3 ≤ m ≤ 10.†

(a) Calculate the amplitude and average value of the model. (Round your answer to one decimal place.)

amplitude		lizards
average value		lizards

(b) Calculate the highest and lowest monthly harvests. Write a sentence interpreting these numbers in context. (Round your answer to the nearest integer.)

The most lizards harvested in one month is lizard(s) and the least harvested in one month (during harvest season) is lizard(s).

(c) Calculate the period of the model. (Round your answer to three decimal places.)

Answer 1

The general equation for a sine function is

y = AsinB(x + C) + D

A = amplitude

B = 2*pi/period

C = phase (or horizontal shift: right if positive, left if negative)

D = average value

Applying this information to the given equation:

A = 15.3

B = 0.805 ==> period = 2*pi/0.805 = 7.805

Average value = D = 16.7

Max value = D + A = 16.7 + 15.3 = 32

Min value = D - A = 16.7 - 15.3 = 1.4 = 1 (rounded to nearest whole number)