If $P(t)$ is the size of a population at time $t$, which of the following differential equations describes linear growth in the size of the population?

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Linear growth is given by the familiar equation:

$$y=mx+b$$

Using the corresponding variables:

$$P(t)=mt+b$$

Differentiation with respect to time:

$$\frac{d}{dt} (P(t)) = \frac{d}{dt}(mt+b)$$ $$\frac{dP}{dt}=m$$

Where $m$ is the rate of change.