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The fish population increases according to the logistic curve is , where is measured in months.
(a)
Graph:
Graph the function .
(b) What is the limiting size of the fish population.
The limiting size of the fish population is .
.
The limiting population is .
(c) At what rates is the fish population changing at the end of month and at the end of months.
Apply derivative on each side with respect to .
.
The rate of change of fish population at the end of month.
Substitute in .
.
The rate of change of fish population at the end of month is .
The rate of change of fish population at the end of months.
Substitute in .
.
The rate of change of fish population at the end of months is .
(d) After how many months is the population increasing most rapidly.
Again apply derivative on each side with respect to .
.
The maximum value of occurs at .
Apply log on each side.
.
The population increasing most rapidly after months.
(a)
Graph:
Graph the function .
(b) The limiting population is .
(c)
The rate of change of fish population at the end of month is .
The rate of change of fish population at the end of months is .
(d) The population increasing most rapidly after months.
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