Modeling Applications and Diff EQs

[neshepard]

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.

 

[fzero]

It's correct up to some parentheses you left out.

 

[neshepard]

P(t)=1000/(1+3e^-.00005t) are these the parentheses you mean?

Thanks

 

[fzero]

P(t)=1000/(1+3e^-.00005t) are these the parentheses you mean?

Thanks

Almost, I'd put parenthesis around the exponent as well

P(t)=1000/(1+3e^(-.00005t))

It's much easier to read that way.

 

[neshepard]

Thanks. Staring to long at this.