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Math / Differential Equations and Linear Algebra 3 / Chapter 2.1 / Problem 20P

Differential Equations and Linear Algebra | 3rd Edition | ISBN: 9780136054252 | Authors: C. Henry Edwards, David E. Penney

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Solved: Consider an alligator population P(t) satisfying

Chapter 2, Problem 20P

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QUESTION:

Problem 20P

Consider an alligator population P(t) satisfying the extinction/explosion equation as in Problem 18. If the initial population is 110 alligators and there are 11 births per month and 12 deaths per month occurring at lime t = 0, how many months does it take for P(t) to reach 10% of the threshold population M?

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QUESTION:

Problem 20P

Consider an alligator population P(t) satisfying the extinction/explosion equation as in Problem 18. If the initial population is 110 alligators and there are 11 births per month and 12 deaths per month occurring at lime t = 0, how many months does it take for P(t) to reach 10% of the threshold population M?

ANSWER:

Solution:

Step 1 of 2

In this problem, we have given that ${P}_{0}=110$ , ${B}_{0}=11$ and ${D}_{0}=12$

The alligator population $P(t)$ satisfying the extinction-explosion equation

$\frac{dP}{dt}=a{P}^{2}-bP$

We can write $\frac{dP}{dt}=aP(P-\frac{b}{a})$

Comparing the above equation with $\frac{dP}{dt}=kP(P-M)$ , where $M=\frac{b}{a}$

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