Question $2(10$ pts$).$ Verify using first principles that the following equation governing bacterial

population $N$ in a Petri dish is non$-$linear:

$\frac{dN}{(d)t}=kN(1-\frac{N}{N_{\text{m}\text{a}\text{x}}})$

where $k$ and Nugat are fixed parameters. $($Hint: Use properties of additivity and proportionality$)$