Hi. Area = A is a function of time, i.e. A(t)
It is the area of the weed at any given point in time (in month). The rate at which the weed grows is the rate of change of area. A'(t).
Hence, because it is said that A is proportional to A', and the area not occupied (which is total area minus the A), you can substitute the equation
A(t) = k.A'(t).(10-A)
Remember the "k", the proportionality constant