A mathematical model for population growth over short intervals is given by $P=P_0{e}^{rt},$ where $P_0$ is the population at $t=0,r$ is the continuous compound rate of growth, $t$ is the time in years, and $P$ is the population at time $t.$ Some underdeveloped nations have population doubling times of $44$ years. At what continuous compound rate is the population growing?

Substitute the given values into the equation for the population. Express the population at time t as a function of $P_0$

$P_0=P_{0}lon,(Simplify$ your answers.$)$