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.