Application of Differential Equation - Practice Questions & MCQ

Differential equations are used in a variety of disciplines, such as biology, economics, physics, chemistry, and engineering.

Growth and Decay Problem:

Let the amount of substance (or population) that is either growing or decaying be denoted by N(t).  if we assume  the time rate of change of this amount of substance, dN / dt,  is proportional to the amount of substance present, then

$\frac{d N}{d t}=k N \quad$ or $\quad \frac{d N}{d t}-k N=0$

Where k is the constant of proportionality. We are assuming that N(t) is a differentiable, hence continuous, function of time.