The population model

$\frac{dP}{dt}$propP, $or,\frac{dP}{dt}=kP$

fails to take death into consideration; the growth rate equals the birth that is$,$ the difference between the rate of births and the rate of deaths present at time $t>0.($Assume the constants of proportionality for the $b$

$\frac{dP}{dt}=$

$$