3. There is a population of deer in Algonquin Park. The average population is 2500, but is declining by 600 per year (or 50 per month). There is periodic variation in the population of plus or minus 1000 as the seasons change; the lowest population is in midwinter at the start of the year.

a) Make a model for the average population of deer using time in months. (Starts at 2500 and declines by 50 per month.)

b) Make a model for the seasonal variation of the deer, using time in months. It varies by plus or minus 1000 with a period of 12 months and the minimum is at the starting point.

c) Make a model for the total population of deer by combining the average population and seasonal variation into one function.

d) Estimate when the population of deer will fall below zero. You may work this numerically or graphically. Explain and justify your solution.