A population of bacteria in a Petri dish is modeled by $P^{\prime }\left(t\right)+aP\left(t\right)=S$, where $P\left(t\right)$ is the population at time $t$ (in hours), $a$ is the death rate constant, and $S$ is the supply rate. If $S=40$ cells per hour and $a=0.2$ per hour, what is the equilibrium population?

• A. $100$ cells
• B. $200$ cells
• C. $80$ cells
• D. $120$ cells