Question: The population of a herd of deer is modeled by
P(t) = 4000 + 500 sin(2Πt - (Π/2))
where t is measured in years from January 1.
(a) How does this population vary with time? Sketch a graph of P(t) for one year.
(b) Use the graph to decide when in the year the population is a maximum. What is that maximum? Is there a minimum? If so, when?
(c) Use the graph to decide when the population is growing fastest. When is it decreasing fastest?
(d) Estimate roughly how fast the population is changing on the first of July.