". 4. The size of the population (P) of migrating birds in a particular town can be approximately modelled by the equation P = a sin(bt) + c, a, b, c E R*, where t is measured in months from the time of the initial measurements. In a 12 month period the maximum population is 2600 and occurs when t = 3 and the minimum population is 800 and occurs when t - 9. This information is shown on the graph below. (3, 2600) (9, BOO) 12 a. [2 marks) Find the value of a. 4b. [2 marks) Find the value of b. 4c. [1 mark] Find the value of c. 4d. [2 marks) Find the value of t at which the population first reaches 2200