Discussion
Which one of the following formula gives doubling time (t) of a given population ?
Answer: B
The doubling time of a population is the natural logarithm of 2 divided by the growth rate r, which is the second option.
If a population grows at a constant rate r, then \[ P_t = P_0 e^{rt} \]
Setting the population equal to double the starting value gives \[ 2 = e^{rt} \]
Taking natural logarithms of both sides gives \[ t = \frac{\log_e 2}{r} \]
The first option uses the logarithm without the base e, which would give a different number, and the third and fourth options have 2r in the denominator, which would make the doubling time half as long, so they are wrong. The 2 printed above the log in the booklet stands for the number 2 whose logarithm is taken.
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