MODERATE EXERCISES-Modelling with Trigonometric Functions

(2) A population of animals varies sinusoidally between a low of 700 on January 1 and a high of 900 on July 1.

1. Graph the population against time.
2. Find a formula for the population as a function of time, t, measured in months since the start of the year.
3. According to your formula, what is the population on March 15?

HINT: First, let t=0 correspond to January 1, where t is in months.  Then you
 can work out the period from the information in the problem -- half the period of a
 trig function lies between a trough and a crest.  Then you can work out the vertical
 "center" of the population and the amplitude.


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