Population Dynamics: Example1
Example: Let P(t) be the population of a certain animal species.
Assume that P(t) satisfies the logistic growth equation
.

 1.
 Is the above differential equation separable?
 2.
 Is the differential equation autonomous?
 3.
 Is the differential equation linear?
 4.
 Without solving the differential equation, give a sketch of
the graph of P(t).
 5.
 What is the longterm behavior of the population P(t)?
 6.
 Show that the solution is of the form
Find A and B.
Hint: Use the initial condition and the result of 5.
 7.
 Where is the solution's inflection point?
Hint: This can be done without using the answer of 6.
 8.
 What is special about the growth rate of the population
P(t) at the inflection point (found in 7)?
Solution:
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