A population of rabbits oscillates 30 above and below averag

A population of rabbits oscillates 30 above and below average during the year, hitting the lowest value in January (t = 0). The average population starts at 650 rabbits and increases by 8% each month. Find an equation for the population, P, in terms of the months since January, t.

Solution

intial population : Po = 650

period = 2pi/12 = pi/6

trigonometric component = - 30cos(pi*t/6)

There is an exponential growth component : 650(1.08)^t = 650(1.08)^t

So, P(t) = - 30cos(pi*t/6) + 650(1.08)^t