Math 22 Exponential Growth and Decay

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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 $k>0$ and exponential decay by $k<0$.

Guidelines for Modeling Exponential Growth and Decay

 1. Use the given information to write two sets of conditions involving $y$ and $t$
 2. Substitute the given conditions into the model 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 y=Ce^{kt}}
 and 
 use the results to solve for the constants 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 C}
 and 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}
.
 3. Use the model 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 y=Ce^{kt}}
 to answer the question.

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