SOLUTION: A computer purchased for $650 loses 18% of its value every year. The computer's value can be modeled by the function v(t)=a⋅b^t, where v is the dollar value and t the numb

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Question 1132235: A computer purchased for $650 loses 18% of its value every year.
The computer's value can be modeled by the function v(t)=a⋅b^t, where v is the dollar value and t the number of years since purchase.
In the exponential model a = , b =
In how many years will the computer be worth half its original value? Round answer to 1 decimal place.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
a, the initial purchased value, $650.

b, loss of 18% of value per year, 1-0.18=0.82.


v=ab%5Et
for halving the value,
1b%5Et=1%2F2
log%28%28b%5Et%29%29=log%28%281%2F2%29%29
t%2Alog%28%28b%29%29=log%28%281%2F2%29%29
t=log%28%281%2F2%29%29%2Flog%28%28b%29%29
t=log%28%281%2F2%29%29%2Flog%28%280.82%29%29
t=3.5years