Question: Consider a population whose number we denote by PP. Suppose that bbis the average number of births per capita per year and ddis the average

Consider a population whose number we denote by PP. Suppose that bbis the average number of births per capita per year and ddis the average number of deaths per capita per year. Then the rate of change of the population is given by the following differential equation,dPdt=bPdP,(1)dPdt=bPdP,(1)where ttis the time (in years).(a)Suppose that b=12b=12and d=7d=7. Solve the above ODE subject to the initial condition P(0)=500P(0)=500, and enter your expression for P(t)P(t)below:

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