SOLUTION: A laptop computer is purchased for $2700. Each year its value decreases by 20%. After how many years will the laptop first be worth under $900?

Question 883415: A laptop computer is purchased for $2700. Each year its value decreases by 20%. After how many years will the laptop first be worth under $900?
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
(1 - % decrease)^x = 900
where x is the number of years
2700*(0.80)^x = 900
divide each side by 2700
(0.80)^x = 900/2700
(0.80)^x = 1/3
Take log of each side
log((0.80)^x) = log(1/3)
x*log(0.80) = log(1/3)
divide each side by log(0.80)
x = log(1/3)/log(0.80) = 4.923..
Let's check 2700*(0.80)^4.923 = 900.69.. so we are close
In just under 4.93 years we will have a value under $900
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