The first prize for the World Series of Pokers main event ha

The first prize for the World Series of Poker\'s main event has grown approximately exponentially from $0.19 million in 1975, when the event began, to $8 million in 2006. Use your calculator to find the regression equation for the function P(x), where P is the value of the first prize and x is the year after 1975. Find the year in which the first prize will reach $25 million.

Solution

0.19 million in 1975

8 million in 2006

So, its exponential growthso, use an expoenetila model:

P(x) = a(b)^x .Find the equation using two points : ( 0, 0.19) , ( 31, 8)

So, a = 0.19

So, P(x) = 0.19(b)^x ; 8 = 0.19(b)^31

b =(42.10)^1/31 = (42.10)^0.03225 = 1.128

So, P(x) = 0.19(1.128)^x

in which year P(x) = 25 mill

So, 25 = 0.19(1.128)^x

x = 40.51 years

It means year 2016