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let the population of rabbits surviving at a time be governed by the diffrential equation  dp(t)/dt =1/2  p(t) - 200. if p(0)=100 then p(t) =  
Asked by ppavani198 | 19 Dec, 2018, 09:09: PM
answered-by-expert Expert Answer
begin mathsize 12px style fraction numerator d p over denominator d t end fraction equals 1 half p minus 200 space equals space fraction numerator p minus 400 over denominator 2 end fraction fraction numerator d p over denominator p minus 400 end fraction space equals space fraction numerator d t over denominator 2 end fraction B y space i n t e g r a t i n g space b o t h space s i d e s comma space w e space g e t space comma space space space ln open square brackets p space minus space 400 close square brackets space equals space t over 2 space plus space C open square brackets p space minus space 400 close square brackets space equals space C space e to the power of bevelled t over 2 end exponent p space equals space 400 plus C space e to the power of bevelled t over 2 end exponent w h e n space t space equals space 0 comma space p space equals space 100 space colon space space H e n c e space space 100 space equals space 400 plus C space space semicolon space space h e n c e space C space equals space minus 300 space semicolon p left parenthesis t right parenthesis space equals space 400 space minus space 300 space e to the power of bevelled t over 2 end exponent end style
Answered by Thiyagarajan K | 19 Dec, 2018, 10:42: PM

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