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A species population P(t) evolves as dP/dt = 0.5P - 450 with P(0) = 850. At what time does the population reach zero?
- logₑ 18
- logₑ 9
- (1/2) logₑ 18
- 2 logₑ 18
Correct answer: 2 logₑ 18
Solution
Solving gives P(t) = 900 - 50 e^(0.5t). P = 0 gives e^(0.5t) = 18, so t = 2 ln 18.
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