
Concept explainers
(a)
Find the population of the wolves after one year, evaluate p1=0.45+1.5(0.45)(1−0.45)
(a)

Answer to Problem 48SR
The population of wolves after 1 year is 0.82125
Explanation of Solution
Given:
In a particular forest, scientists are interested in how the population of wolves will change over the next two years. One model for animal population is the Verhulst population model, pn+1=pn+r pn(1−pn) where n represents the number of time periods that have passes pn represent the percent of the maximum sustainable population that exists at time n, and r is the growth factor.
To find the population of the wolves after one year, evaluate p1=0.45+1.5(0.45)(1−0.45)
Concept Used:
Evaluate: p1=0.45+1.5(0.45)(1−0.45)
Calculation:
p1=0.45+1.5(0.45)(1−0.45)=0.45+0.675 · 0.55=0.82125
Thus, the population of wolves after 1 year is 0.82125
(b)
Explain what each number in the expression in part a represents.
(b)

Answer to Problem 48SR
0.45 represents the maximum sustainable population of 45 % and 1.5 is the growth factor.
Explanation of Solution
Given:
In a particular forest, scientists are interested in how the population of wolves will change over the next two years. One model for animal population is the Verhulst population model, pn+1=pn+r pn(1−pn) where n represents the number of time periods that have passes pn represent the percent of the maximum sustainable population that exists at time n, and r is the growth factor.
Explain what each number in the expression in part a represents.
Concept Used:
0.45 represents the maximum sustainable population of 45 % and 1.5 is the growth factor.
Thus, 0.45 represents the maximum sustainable population of 45 % and 1.5 is the growth factor.
(c)
Find the new population by multiplying 165 by the value in part a.
(c)

Answer to Problem 48SR
The new population of wolves is about 136.
Explanation of Solution
Given:
In a particular forest, scientists are interested in how the population of wolves will change over the next two years. One model for animal population is the Verhulst population model, pn+1=pn+r pn(1−pn) where n represents the number of time periods that have passes pn represent the percent of the maximum sustainable population that exists at time n, and r is the growth factor.
The current population of wolves is 165. Find the new population by multiplying 165 by the value in part a.
Concept Used:
New population = 165 · 0.82125≈ 136 wolves.
Thus, the new population of wolves is about 136.
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