TEXP31 Fish population on a fish farm follows the logistic curve (use base e and t is in months).
The farm will support a maximum of 2000 fish. You start the farm (t = 0 is the first month) with 100 fish.
Find the specific logistic function and the fish population at four months (t = 3).
Find the rate of increase in fish population at this time (t = 3).
Solution: If the farm will support 2000 fish, then for t very large the Be-t term goes to zero and N = 2000.
When t = 0, there are 100 fish so write the statement for this situation and solve for B.
Now write the specific equation for the logistic model for this fish farm.
Now find the number of fish for t = 3, month 4.
Now differentiate to find the general expression for the rate of fish growth.
Put in the numbers and evaluate the rate of fish population growth at t = 3.
