Differential Equation Problem

Here are the solutions to the problems.

12. Differential Equation Problem

a) (i) Form a differential equation for the rate of increase in the quantity of the commodity demanded.
The rate of increase in quantity $N$ with respect to time $t$ is $\frac{dN}{dt}$.
It is inversely proportional to the quantity $N$.

$$\frac{dN}{dt} \propto \frac{1}{N}$$

Introducing a constant of proportionality $k$:

$$\boxed{\frac{dN}{dt} = \frac{k}{N}}$$

a) (ii) Solve the differential equation.