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

#2**0 **

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)

CPhill
Mar 17, 2017