Question

A biologist tracked the deer population in a rural area of Wisconsin and found that the deer population in this area was cyclic. He used his data to find a function to approximate the population over a year long period. The function g defined by g(t) = 1125-875cos(pi/6t), 0 < t < 12, represents the number of deer g(t) in terms of the number of months t since November 1, 2009. Use the arccosine function to determine the number of months in which the deer population was at least 600.

Answer 1

first, find where it is equal:
1125-875cos(π/6 t) = 600
875 cos(π/6 t) = 525
cos(π/6 t) = 0.6
π/6 t = arccos(0.6) = 0.9273
t = 0.9273 * 6/π = 1.77
since the period of g(t) is 12, this is also true at 12-1.77
so, you want 1.77 <= t <= 10.23