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Lecture

# 9.4 Population Growth Model Question #2 (Medium)

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University of Toronto St. George

Mathematics

MAT136H1

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Winter

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9.4 Differential Equations
Population Growth Model
Question #2 (Medium): Setting the Logistic Differential Equation
Strategy
The logistic differential equation is: ( ) which shows the rate of population growth over
time incorporating the carrying capacity and growth rate k factor, which can be calculated by
by plugging in the birth rate over death rate as and initial population of .
Sample Question
Population at a small town by a mountain is about in 2013.
Birth rates range from to per year, and death rates range from to per year.
Assume that the carrying capacity for the town’s population is .
1) Write the logistic differential equation for the given data.
2) Use the logistic model to estimate the town’s population by 2017.
3) How would the future forecast change if the carrying capacity is ?
Solution
1) Given the logistics model of ( ), where the carrying capaci

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