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The population P = P(t) at time 't' of a certain species follows the differential equation dP/dt = 0.5P − 450. If P(0) = 850, then the time at which population becomes zero is, (1) log_e 18 (2) log_e 9 (3) 1/2 log_e 18 (4) 2 log_e 18

1. log_e 18
2. log_e 9
3. 1/2 log_e 18
4. 2 log_e 18

Correct answer: 2 log_e 18

Solution

The correct option is right because solving the differential equation leads to an exponential model for the population, and substituting the initial condition allows us to find the time when the population reaches zero, which is calculated to be 2 log_e 18.

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