What is the population of rabbits in September?

Question

A population of rabbits is at its lowest in January (t=0) and oscillates 21 above and below an average of 149 during the year.

What is the population of rabbits in September?

Answer 1

y = Asin(Bt) + C, where t = number of months since January and y = population in month t.

A = 21, C = 149, Period = 12 = 2π/B. So, B = π/6.

y = 21sin [ (π/6)t ] + 149

Population in September (I.e., when t = 9) is 21sin(3π/2) + 149 = 21(-1) + 149 = 128.