The initial mass of fish in a lake was 7 thousand pounds on January 1st, 2001. Since the time, there was a 4-year moratorium on the harvesting on this specific type of fish. This species of fish reproduce at a rate proportional to the mass and by next year on the same date, there were 11.54 thousand pounds of fish.
After the moratorium (2005) ends, a certain company is given exclusive rights to harvest 24 thousand pounds of fish per year from the lake.
I need to set up a Diff Eq. modeling the mass of the species of fish in thousands at time T (T in years), and T=0 on Jan. 1 2001. Then a solution for the differential equation must be found.
The only way I know to start off is:
dC/dT = Rate In - Rate Out
The Attempt at a Solution
the first reproduce at rate prop. to mass. and we model the fish using mass, so.
dM/dt = aM where M is the total mass of fish and a is some constant.
that was before the moratorium.
24000 lb fish harvested per year. so
dM/dt = aM - 24000 after the moratorium.
After this, I am rather confused and lost.