Question

A population of rabbits oscillates 18 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 160 each year. Find an equation for the population, P, in terms of the months since January,

Answer 1

There are two functions here

trigonometric and exponential function

Trigonometric function:

we can use formula

we are given

A=-18

T=12

now, we can plug values

Exponential function:

we can use formula

a=650

at t=1, f(t)=650+160=810

we can plug it

now, we can find function

...........Answer