Engineering Board Exam Reviewer · Applications: Growth and Decay · hard
A population obeys the logistic equation dP/dt=0.1P≤ft(1-P/1000 ) with P(0)=100. Find P(10).
- 213.7
- 271.8
- 999.6
- 232
Answer
D. 232
Solution
The solution of P'=kP(1-P/K) is P= K1+Ae-kt with A=K-P0/P0=9. So P= 10001+9e-0.1t and P(10)= 10001+9e-1 231.9.
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