plz solve this application problem involving separate integral?

summerhill

2009-11-03 8:12 am

The rate of growth satisfies the equation:
(dR/dt)= kR (L-R)
FIND: R(t)
given: L=500, R(0)=5, and K= 0.0001

I don't know how to isolate the R-items out in order to obtian R(t) after doing partial fraction decomposition.

回答 (1)

[匿名]

2009-11-03 11:40 am

✔ 最佳答案

HINTS
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[ 1 ]

Use Partial Fractions :

1 / [ R ( L - R ) ] = ( 1 / L ) [ ( 1 / R ) + ( 1 / (L-R) ) ].
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[ 2 ]

1. ∫ ( 1 / R ) dR = ln (R )

2. ∫ [ 1 / ( L - R ) ] dR = - ln ( L - R ).
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Now, you can easily manage the rest.
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