An ecologist studying a species of water beetle estimates th

An ecologist studying a species of water beetle estimates the population of a colony over an eight week period. If t is the number of weeks after the initial estimate is made, then the population in thousands can be modeled by P (t) = 5 + 2 sin(pi t/2) where 0 lessthanorequalto t lessthanorequalto 8. a What was the initial population? b What were the smallest and largest populations? c During what time interval(s) did the population exceed 6000?

Solution

P(t) = 5 + 2sin(pi*t/3)

a) intial pop : t =0

P(0) = 5

b) smallest population = 5- 2 = 3

largest population 5 + 2= 7

c)    P(t() > 6

6 > 5 + 2sin(pi*t/3)

0.5 < t < 2.5