Answer to Question #267521 in Differential Equations for charlotte

Question #267521

exponential growth and decay formula and graph


1
Expert's answer
2021-11-17T18:06:33-0500

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


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

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


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




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


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

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