SOLUTION: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purch
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-> SOLUTION: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purch
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Question 128802: Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value??? Please HELP me :) Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Michael purchases a rare coin for $100 that will double in value every 9 years. His friend John purchases a rare book for $75 that will double in value every 6 years. If both purchases were made at the same time, in how many years will they be of equal value???
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Coin DATA:
Value = 100*(2^t/9)
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Book DATA:
Value = 75*(2^t/6)
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EQUATION:
value = value
100(2^(t/9)) = 75(2^(t/6))
2^(t/6-t/9) = 100/75
2^(3t/54) = 4/3
2^(t/18) = 4/3
Take the log of both sides to get:
(t/18)log(2) = log(4/3)
t/18 = 0.4150
t = 7.47 years
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Cheers,
Stan H.
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