The simplest first order models are those in which the rate of change of the population is proportional to the current population. These processes can either represent growth $($if the proportionality constant is positive$)$ or decay $($if the proportionality constant is negative$).$ The equations below give the differential equation for a population which grows exponentially, together with the solution:dPdt$=$rPP$(0)=$P$0$P$($t$)=$P$0$ert

Growth rates are often given in terms of doubling times: A doubling time of seven years means that after seven years have passed the population is twice the original population.

If the doubling time for a particular model is T$=13$ years, find the constant r$.$

r$=$yr$1$