Question

Suppose that a population has a growth rate of r per member in unit time, with r>0.

Show that the time required for the population to double its initial size (called the doubling time) is (log2)/r.

Answer 1

Answer: Hello there!

A model to see the growth of a certain population is the exponential model.

If the initial population is P, then the model can be written as

$f(t) = Pe^{rt}$

Where t is the time, and r is growth rate.

and f(0) = P

Then we want to know the time needed for the initial population to be doubled, this is f(x) = 2P, where x is the time that we want to find.

then $f(x)=Pe^{rx} =2P$

$e^{rx} = 2$

$ln(e^{rx} ) = ln(2)$

$rx = ln(2)$

then x= ln(2)/r