Fox Population Problem: 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 years. A minimum number of 200 foxes appeared when t = 2.9 years. The next maximum, 800 foxes, occurred at t = 5.1 years. a. Sketch the graph of this sinusoid. b. Find a particular equation expressing the number of foxes as a function of time. c. Predict the fox population when t = 7, 8, 9, and 10 years. d. Foxes are declared an endangered species when their population drops below 30 Between what two nonnegative values of t were the foxes first endangered? e. Show on your graph in part a that your answer to part d is correct.
Step 1 of 4
a) Use the data given in the question to sketch the sinusoid as shown below:
As seen, the population is minimum at years and is maximum at years.