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Let the population of rabbits surviving at time t be governed by the differential equation dp(t)/dt = 1/2 p(t) - 200. If p(0) = 100, then p(t) equals:
- 600 - 500 e^(t/2)
- 400 - 300 e^(-t/2)
- 400 - 300 e^(t/2)
- 300 - 200 e^(-t/2)
Correct answer: 400 - 300 e^(t/2)
Solution
dp/dt - p/2 = -200 has solution p(t)=400+C e^(t/2). Using p(0)=100 gives C=-300, so p(t)=400-300 e^(t/2).
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