How To: Use differential equations to represent growth

Use differential equations to represent growth

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.

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