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neshepard
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Homework Statement
A certain virus spreads through an entire population of 1000. It is assumed that the virus spreads at a rate proportional to the product of the infected and the uninfected. k=.00005 and initial infected is 250. Write and solve the diff eq for this problem.
Homework Equations
I used dP/dt=kP(1-P/L) where P=infected population, L=1000 carrying capacity, k=constant
The Attempt at a Solution
dP/dt=.00005P(1-P/1000)
dP/P(1-P/1000)=.00005dt and integrate both sides to get
P(t)=1000/1+3e^-.00005t
Is this correct? Maybe I'm just tired, but looking at it seems weird somehow.