Consider a Population $P = P ( t )$ With Constant Relative Birth and Death Rates

Consider a population $P = P ( t )$ with constant relative birth and death rates $a$ and $\beta$ , respectively, and a constant emigration rate $m$ , where $\alpha = 0.6 , \beta = 0.9$ and $m = 0.7$ . Then the rate of change of the population at time $t$ is modeled by the differential equation
$$\frac { d P } { d t } = k P - m$$
where
$$k = \alpha - \beta$$
Find the solution of this equation with the rate of change of the population at time $t = 3$ that satisfies the initial condition $P ( 0 ) = 2600$ .