5). Consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells.

P'(t) = ln

K

P

P

Assume that for a population,

K = 1,000

and

= 0.05.

Draw the directional field associated with this differential equation and draw a few solutions.

7) The population of trout in a pond is given by P' = 0.4P

1

P

10,000

f, where f trout are caught per year.

Consider the case where a certain number of fish are added to the pond, or

f = 100.

What are the nonnegative equilibria and their stabilities? (Round your answer to two decimal places.)

P = ___ . ( AND IF THE ITS STABLE OR UNSTABLE )

PLEASE SHOW STEP BY STEP CLEARLY .

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