Question

First prize for the world series of poker's main event has grown approximately exponentially from 0.21 million in 1975 to 8.25 million in 2007. predict when the first prize will be 20million

Answer 1

Sounds like past performance is not indicative of future returns.

Answer 2

huh

Answer 3

Kind of a joke. The WSOP Main Event first prize leveled out after peaking in 2006. http://en.wikipedia.org/wiki/World_Series_of_Poker#Main_Event_results

Anyway, treating this as a math problem, you could say:\[Prize = .21*B^t\] where 1975 is t=0

Answer 4

So that is our first point. At time = 0, the prize is $0.21 M
At time = 33 (2007-1975) Prize was $8.25 M. Or: \[$8.25 M = $0.21 M*B^{33}\]and we need to solve\[$20 M = $0.21 M*B^{x}\]We can do this by solving for B by taking the log of both sides of the first equation.

Answer 5

how would we do that?

Answer 6

\[\frac{8.25}{0.21}=B^{33}\]\[\log{\frac{8.25}{0.21}}=\log{B^{33}}=33\log{B}\]\[\frac{1}{33}\log{\frac{8.25}{0.21}}=\log{B}\]while\[\log{\frac{20}{0.21}}=x\log{B}\]so \[x = 33\frac{\log{\frac{20}{0.21}}}{\log{\frac{8.25}{0.21}}}\]