- #1

cheddacheeze

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## Homework Statement

Consider a population whose number we denote by [tex] P [/tex] . Suppose that [tex]b[/tex] is the average number of births per capita per year and[tex]d[/tex] is the average number of deaths per capita per year. Then the rate of change of the population is given by the following differential equation,

[tex]dP/dt = bP-dP [/tex] where t is in years

[tex]d = 4 + P/200, b = 9 and P(0) = 200[/tex]

solve for [tex]P(t)[/tex]

(Hint: you might find the partial fraction in part (c) useful in determining your solution.)

## Homework Equations

part (c) being:

[tex] 200/P(1000-P) = A/P + B/1000-P [/tex]

A=1/5, B=1/5

## The Attempt at a Solution

[tex]dP/dt = 9P-(4+P/200)[/tex]

[tex]dP/dt = 9P-4-P/200 [/tex]

[tex]dP=(9P-4-P/200)dt[/tex]

[tex]dp/(9P-4-P/200)=dt[/tex]

im thinking the partial fraction comes somewhere in between my 3rd and 4th line but i cant seem to think what factor and exactly where....