Naturalists find that populations of some kinds of predatory animals vary periodically with time. Assume that the population of foxes in a certain forest varies sinusoidally with time. Records started being kept at time t=0 year. A minimum number of 200 foxes appeared at t=2.9 years. The next maximum, 800 foxes, occurred at t=5.1 years. (a). Graph and write an equation expressing the number of foxes as a function of time.
(b). Predict the fox population when t= 7, 8, 9, and 10 years.
(c). Foxes are declared an endangered species when their population drops below 300. Between what two nonnegative values of t did the foxes first become endangered?