Question 243631
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.