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The rabbit population p(t) obeys dp(t)/dt = (1/2) p(t) - 200, with p(0) = 100. Then p(t) equals:
- 400 - 300 e^(t/2)
- 300 - 200 e^(-t/2)
- 600 - 500 e^(t/2)
- 400 - 300 e^(-t/2)
Correct answer: 400 - 300 e^(t/2)
Solution
Solving the linear equation gives p(t) = 400 + C e^(t/2); the initial condition p(0)=100 fixes C = -300, so p(t) = 400 - 300 e^(t/2).
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