Concept explainers
Predator Population Model In a predator/prey model, the predator population is modeled by the function
where t is measured in years.
- (a) What is the maximum population?
- (b) Find the length of time between successive periods of maximum population.
(a)
The maximum population of the predator.
Answer to Problem 30E
The maximum population of the predators is
Explanation of Solution
Given:
The function for the predator’s population is,
Calculation:
The equation for the simple harmonic motion which describes the displacement y of an object at time t is,
For the maximum displacement the cosine function should be maximum. So, the cosine function is maximum at
Substitute 0 for t in equation (1),
Thus, the maximum population of the predators is 8900.
(b)
The time between the successive periods of maximum population.
Answer to Problem 30E
The time between the successive intervals of maximum displacement is 3.14 years.
Explanation of Solution
Given:
The function for the predator’s population is,
Calculation:
The equation for the simple harmonic motion which describes the displacement y of an object at time t is,
Calculate time period for the maximum displacement,
For the maximum displacement the cosine value should be 0. So, the value is,
For the cosine curve the time period is,
Calculate time period for the maximum displacement,
Equate the equation (3) and (4),
Thus, the length of time for the maximum displacement between successive period is
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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