Math 22 Exponential Growth and Decay

Exponential Growth and Decay

 If $y$ is a positive quantity whose rate of change with respect to time
 is proportional to the quantity present at any time $t$, then  is of the form
 $y=Ce^{kt}$
 where $C$ is the initial value and $k$ is the constant of proportionality. Exponential growth is indicated by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k>0}
 and exponential decay by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k<0}
.

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