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Fox Population Problem: Naturalists find that populations of some kinds of predatory

Precalculus with Trigonometry: Concepts and Applications | 1st Edition | ISBN: 9781559533911 | Authors: Foerster ISBN: 9781559533911 468

Solution for problem 2 Chapter 3-7

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Precalculus with Trigonometry: Concepts and Applications | 1st Edition | ISBN: 9781559533911 | Authors: Foerster

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Problem 2

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-by-Step Solution:

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.

Step 2 of 4

Chapter 3-7, Problem 2 is Solved
Step 3 of 4

Textbook: Precalculus with Trigonometry: Concepts and Applications
Edition: 1
Author: Foerster
ISBN: 9781559533911

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Fox Population Problem: Naturalists find that populations of some kinds of predatory