4. When an infected person is introduced into a closed and otherwise healthy community, the number of people who become infected with the disease (in the absence of intervention) may be modeled logistically. On a small secluded island of 300 people, one initially contracts the Coxsackie B virus. The spread of this virus through the island is modeled by the differential equation

dP/dt=0.025P(1P/300) .

a. Solve this differential equation with the given initial condition. Initial condition is implied by the above statement.

b. If time is in days, how long will it approximately take for half the island to be infected?