Answer to Question #267521 in Differential Equations for charlotte

Question

exponential growth and decay formula and graph

Answer 1

The only solutions of the differential equation $dy/dx=ky$ are the exponential functions

$$y(x)=y(0)e^{kx}$$

If $k>0,$ we have an exponential growth.

$$y(x)=y(0)e^{kx}=y(0)e^{|k|x}$$

f $k<0,$ we have an exponential decay.

$$y(x)=y(0)e^{kx}=y(0)e^{-|k|x}$$