Help with this question please

Question

A population of rabbits oscillates 22 above and bellow and average of 76 during the year. hitting the lowest value in January (t=0). Find an equation for the population, P, in terms of the months since January, t.

P(t)=

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

P(t)=

Answer 1

the midline is 76 which is your vertical shift (d)

Amplitude is 22 (a)

Period is 12 months so b=2pi/12 or pi/6

there is no phase shift (c) since you are starting at time 0

Since you start at a minimum value you should model with a negative cosine graph

y= -22cos(pi/6)+76

If the lowest value occurred in the 4th month you have shifted the graph 4 to the right so equation now becomes

y= -22cos[(pi/6)-4] +76