The population sizes of many animal species rise and fall over time. Suppose that the population size of a certain species can be modeled by the following function. P(t) = 3700+ 1100 sin 0.6t In this equation, p (t) represents the total population size, and t is the time in years. Find the following. If necessary, round to the nearest hundredth. Amplitude of p : Time for one full cycle of p : years Number of cycles of p per year:

Given that the population sizes of many animal species rise and fall over time. Suppose that the population size of a certain species can be modeled by the following function.

[tex]P(t) = 3700+ 1100 sin 0.6t[/tex]

We know that sin can take values within -1 and +1, hence minimum is

[tex]3700-1100 = 2600[/tex] and maximum is

[tex]3700 +1100 =4800[/tex]

Amplitude p = 1100

Time for one full cycle of p is we have sin repeats its values after 2pi

i.e. the period if starts from 0, ends in [tex]\frac{2\pi}{0.6} =\frac{10\pi}{3}[/tex]

No of cycles p per year= reciprocal of period = [tex]0.3/\pi[/tex]