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?

SOLUTION: 

(a) 


(b) f(t) = 800  - 100cos(t/6)

(c) On March 15 (t = 2.5 months), the population is 774


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