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baddinlol

  • 3 years ago

Differential equation question; if dp/dt = P-kP where P is population of rabbits. In a certain year the population is too high and they decide to shoot "S" rabbits each year. Therefore dp/dt = P-kP - S. Find in terms P and k the maximum amount of rabbits that can be shot each year to make the population stable.

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  1. akash809
    • 3 years ago
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    \[dp/p=(1-k)dt\] ----> \[\ln p=(1-k)t + c\] equation of population before shooting after shooting ln p=(1-k-s)t + k ...differentiate it, get expression of s and equate it to zero to get the answer

  2. baddinlol
    • 3 years ago
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    So do i equate dp/dt to 0?

  3. akash809
    • 3 years ago
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    \[1/p=1-k-s\]

  4. akash809
    • 3 years ago
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    sorry for previous reply...dont do dp/dt but get expression of s and do ds/dt

  5. baddinlol
    • 3 years ago
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    OK thanks

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