The market value of the 1964 - 1965 Lamborghini 350 GT has had a recent upswing. The car's value increased from $66,000 in 1999 to $220,000 in 2009 (Source: "1964-1965 Lamborghini 350 GT," by David La Chance, Hemmings Motor News, July, 2010,). Assuming that the value V0 of the car has grown exponentially:
a) Find the value of k, and determine the exponential growth function, assuming V0 = 66,000 and t is the number of years since 1999.
b) Estimate the value of the car in 2011.
c) What is the doubling time for the value of the car?
d) After how long will the value of the car be $300,000, assuming there is no change in the growth rate?