MATH241 Lecture 35: Chapter 9 and Review
25 May 2018
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MATH241 - Lecture 35 - Chapter 9 and Review
Chapter 9: Separable Equations and Models of Population Growth (continued)
Example:
Suppose a population satisfies
0400012
050
Where is measured in years
A) What is the carrying capacity?
B) Graph the directional field of the differential equation and plot the solution
corresponding to the initial condition
C) What is ′0?
D) When will the population reach 50% of the carrying capacity?
Solution:
A) 𝑑𝑑
1
Convert to model form
0400012
→ 𝑑𝑑
2
5 1
1000 2
→ 𝑑𝑑
2
515
2000
→ 𝑑𝑑
2
51
400
Thus the carrying capacity is 400
B)
C) 𝑑
1
