Any ideas on how to do this?

Question

During the period between 2001-2011, the average price of an ounce of gold doubled every 4 years. In 2001, the average price of gold was about $270 per ounce.

 

^{Year      Average Price of an Ounce of Gold}

2001             $271.04

2002             $309.73

2003             $363.38 

2004             $409.72

2005             $444.74

2006             $603.46

2007             $695.39

2008             $871.96

2009             $972.35

2010             $1224.53

2011             $1571.52

 

Write an exponential model for the average price of an ounce of gold as a function of time (in years since 2011).

Answer 1

Using the statement "doubled every four years," I am going to ignore the table.

 

f(x) = ab^x, taking 2001 price at 270

f(x) = 270b^x, for the fourth year

540 = 270b⁴

2 = b⁴

2^1/4 = b

 

f(x) = 270(2^1/4)^x