- #1
PCSL
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- 0
I have been trying to figure this problem out for more then 90 minutes and I think I'm past the point where I'm being productive:
A population P satisfies the differential equation:
[tex]P^'(t)=10^{-5}P(t)(15000-P(t))[/tex]
For what value P(0) of the initial population is the initial growth rate P'(0) greatest.
I end up with [tex]\frac{10^5}{P(15000-P)}dP=dt[/tex] which I have no clue how to integrate (I spent most of the 90 minutes trying to figure that out). Before I went on trying to integrate this I want to make sure I didn't set it up wrong. I thought about partial fractions but have no clue how to separate the denominator.
This is the first homework assignment I have ever had for DE and I apologize for posting two threads in two days, I'm trying my best to figure this stuff out.
A population P satisfies the differential equation:
[tex]P^'(t)=10^{-5}P(t)(15000-P(t))[/tex]
For what value P(0) of the initial population is the initial growth rate P'(0) greatest.
I end up with [tex]\frac{10^5}{P(15000-P)}dP=dt[/tex] which I have no clue how to integrate (I spent most of the 90 minutes trying to figure that out). Before I went on trying to integrate this I want to make sure I didn't set it up wrong. I thought about partial fractions but have no clue how to separate the denominator.
This is the first homework assignment I have ever had for DE and I apologize for posting two threads in two days, I'm trying my best to figure this stuff out.