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Lecture

# 9.4 Population Growth Model Question #1 (Easy)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
9.4 Differential Equations Population Growth Model Question #1 (Easy): Population Carrying Capacity Strategy ( ) is known as the logistic differential equation, where is the carrying capacity, and is the relative growth rate constant factor. If the given equation is not in this form, needs to be factored in order to determine and . Sample Question The population follows after the equation, where is in years. , ( ) 1) What is the carrying capacity and the relative growth rate? 2) What is ( ) ? 3) When will the population reach 50% of the carrying capacity? Solution 1) Given the equation, factor out the factor: ( ) ( ). Then comparing to the logistic differential equation form, ( ) ( ), the carrying capacity , and relative growth rate term 2) In order to find ( ) , first ( ) needs to be established. This involves solving the given differential equation: ; ; into partial fractions: , then ( ) ( ) ( ) ; , therefore
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