Differential equations — practice question

A diseased soil infection is spreading across a field with total area $4\text{ km}^2$. After $t$ years, the infected region has area $x\text{ km}^2$, and its growth rate is described by $\frac{dx}{dt} = kx(4 - x)$, where $k$ is a positive constant. It is given that $x = 0.4$ when $t = 0$, and that $x = 2$ when $t = 2$.