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**tiace** A population, $\displaystyle P$, is said to be growing logistically if the time, $\displaystyle T$, taken for it to increase from $\displaystyle P_1$ and $\displaystyle P_2$ is given by:

$\displaystyle \int_{P_1}^{P_2} \frac {kdP}{P(L-P)}$

where $\displaystyle k$ and $\displaystyle L$ are positive constants and $\displaystyle P_1 < P_2 < L$.

A) Calculate the time taken for the population to grow from $\displaystyle P_1 = \frac {L}{4}$ to $\displaystyle P_2 = \frac {L}{2}$.

B)What happens to $\displaystyle T$ as $\displaystyle P_2$ approaches $\displaystyle L$?

I honestly have no clue how to even start this problem. Any help would be appreciated.

Thanks!