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Topic: log growth prob
Replies: 5   Last Post: May 1, 1998 12:32 PM

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Blanchard, Charles

Posts: 8
Registered: 12/6/04
log growth prob
Posted: Apr 28, 1998 4:32 PM
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Ms. Ghitelman. (I concur with your results.)
Concerning your separable differential equation dR/dt=0.001R(200-R)
with initial conditions R(0)=25. After separating, use partial
fractions to integrate 1/(R(200-R)) with respect to R and get
(1/200)(lnR-ln(200-R))or (1/200)ln(R/(200-R)). So the solution to
the differential equation is R/(200-R)=e^(.2t+k). When t is 0, we have
k=ln(1/7), so the implicit relationship between R and t is
R/(200-R)=(1/7)e^(0.2t). Now when R=50, t is about 4.24 . So it
takes about 4.24 weeks to double from 25 rabbits to 50. So the (c)
choice is the correct one (unless I errored somewhere along the way.)

Cade, LA

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