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 long-term 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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