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 $k>0$ 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 $y=Ce^{kt}$ and 
 use the results to solve for the constants $C$ and $k$.
 3. Use the model $y=Ce^{kt}$ to answer the question.

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