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A certain quantity Q has initial value 200 and decays by 20% each year. Give an exponential function that describes this quantity. (Use t in years as your variable.)
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idenny  Mar 17, 2017
 #1
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CPhil I got the answer. It is 

 

200*.80^t

idenny  Mar 17, 2017
 #2
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First year = 200

Second year = 200(1 - .20)  = 200(.80)  = 160

 

So we have

 

160  = 200 * e^(k *1)      divide both by 200

 

160 / 200 = e^(k)

 

4/5  =  e^(k)          take the ln of both sides

 

ln (4/5) = ln e^(k)

 

k =  ln (4/5)  = -0.2231435513142098

 

So the function  is .....     200e^(-0.2231435513142098 * t)

 

 

cool cool cool

CPhill  Mar 17, 2017

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