- #1
cheddacheeze
- 42
- 0
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 can't seem to think what factor and exactly where...