The rate of growth of a population of mice over a 3-year period is given approxi

Question

The rate of growth of a population of mice over a 3-year period is given approximately by

P(t)=2-3cos(pi*t/6) (0?t?36)

Where P(t) is the monthly population growth (in hundreds) t months after February 1st.

Because this is already a rate of change I am having issued determining the following parts:

A. In what month(s) is the population growth growing fastest? (is this P'(t) or P''(t)?)
B. In what month(s) is the population growing fastest? (is this P(t) or P'(t)?)
C. K. Find the average growth of the field mouse population each month from t=24 to t=36. (Is this the 1/(b-a) Integral from a to b of P(t)?)


Thank you!

Explanation / Answer

A. In what month(s) is the population growth growing fastest? (is this P'(t) or P''(t)?

P(t)=2-3cos(pi*t/6) (0t36)

take derivative

P'(t) = -3* - sin(pi*t/6) * pi/6

= pi/2 sin(pit/6) = 0

pi *t/6 = 2npi

t/6 = 2n

t = 12 n

at n = 1

t = 12

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