How to Use differential equations to represent growth

This video shows the method to use differential equations to represent growth. Consider the function y=multiple of C & e raised to kx or Ce^(kx). Differentiating it with respect to x, we get dy/dx=kCe^(kx) or ky. So, the solution of the differential equation dy/dx=ky is Ce^(kx). There are two possibilities in the function y=e^(kx). It can be exponentially growth or decay function. This depends on the value of k. If k is greater than 0 or k>0, we get an exponential growth function. On the other hand if k<0, we get an exponential decay function. The graph of y= Ce^(kx) goes upwards towards the positive y axis if C is positive and vice versa. k is called as the continuous growth rate.