Question 243631: an ad for a special baseball card that was posted on the internet cloaims 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?
Thank you
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! To say that a value doubles every year means that it will go up in value by 2, 4, 8, 16, 32, etc. Notice that those are 2 raised to the 't', where 't' = years numbered 1, 2, 3, 4, 5, etc.
.
f(x) = future value
P = present value = $40
t = year - 2001, which means t will take on values 0, 1, 2, 3, 4, 5, etc.
Note that an exponent of 0 means the value is 1.
.
f(t) = P*2^t
.
year...t...f(t)
2001...0...40
2002...1...80
2003...2...160
2004...3...320
2005...4...640
2006...5...1280
2007...6...2560
2008...7...5120
.
So the card first reaches $5000 value in 2008.
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