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

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