SOLUTION: an ad for a special baseball card that was posted on the itnernet claims that the value of the card "doubles every year." Jerome buys the card for 40$ at the end of the year 2001.

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Question 257715: an ad for a special baseball card that was posted on the itnernet claims that the value of the card "doubles every year." Jerome buys the card for 40$ at the end of the year 2001. If the value of the card does indeed double every year, in what year will the value of the card first reach $5000
Answer by dabanfield(803) (Show Source):
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an ad for a special baseball card that was posted on the itnernet claims that the value of the card "doubles every year." Jerome buys the card for 40$ at the end of the year 2001. If the value of the card does indeed double every year, in what year will the value of the card first reach $5000
The value of the card after the nth year is 40*2^n.
We need to see what is the smallest value of n in the ablove formula gives us at least 5000.
Set 40*2^n = 5000
Divide both sides by 40:
2^n = 125
Take the log of both sides:
log (2^n) = log (125)
n*log (2) = log (125)
n = log(125)/log(2)
n = 2.0967/.3010
n = 6.97 ~ 7 years
The year where the amount passes 5000 is 2001 + 7 = 2008