Taking into consideration the environmental constraints, the rabbit population P

Question

Taking into consideration the environmental constraints, the rabbit population P (in millions now!!) is better described by the differential equation

dP/dt=1/6*P(1P/800)

This is a separable differential equation that can be solved by integrating

8001/(P*(800P))dP=1/6dt.

The solution to this equation is given by

P(t)=800/(1+A*e^(t/6))

where A is a constant determined by the initial conditions. If we let t be the number of years since 1950, then our initial condition becomes P(0)=600. From this we determine that

A= ( )

Explanation / Answer

P(t)= 800/(1+A e -t/6)

P(0)=600

600=800/(1+A e -0/6)

600=800/(1+A e 0)

600=800/(1+A)

1+A=800/600

A=(800/600)-1=200/600=1/3

A=1/3

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