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Let the population of rabbits survivin...

Let the population of rabbits surviving at a time t be governed by the differential equation `d(p(t))/(dt)=1/2p(t)-200.` If `p(0)""=""100` , then p(t) equals (1) `400-300""e^(t//2)` (2) `300-200""e^(-t//2)` (3) `600-500""e^(t//2)` (4) `400-300""e^(-t//2)`

A

`400-300e^(t/(2)`

B

`300-200e^(t/(2)`

C

`600-500e^(t/(2)`

D

`400-300e^(t/(2)`

Text Solution

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A
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Knowledge Check

  • The population of a city increases at the rate 3% per year. If at time t the population of city is p, then find equation of p in time t.

    A
    `p=3e^((3t)/(100)`
    B
    `p=e^((3t)/(100))`
    C
    `p="ce"^((3t)/(100))`
    D
    `p=(3)/(100)e^(3t)`

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