A population of rabbits oscillates 35 above and below an average of 53 during the year, hitting the lowest value in January (t = 0).

Question

What s the equation for the population, P, in terms of the months since January, t.

 = 

IncWhat if the lowest value of the rabbit population occurred in April instead?

 = Incorrect  

Answer 1

P(t) = Asin(Bt + C) + D; D = 53; A = 35; B = 2π/12 = π/6;

At t = 0 P(0) = 53 - 35 = 18; 18 = 35sinC + 53; sinC = -1; C = - π/2.

So, P(t) = 35sin(πt/6 - π/2) + 53.

In april t = 3, P(3) = 35sin0 + 53 = 53