In May 2010, a 1932 painting, Nude, Green Leaves, and Bust, by Pablo Picasso, sold at a New York City art auction for $106.5 million to an anonymous buyer. This is a record price for any work of art sold at auction. The painting had belonged to the estate of Sydney and Francis Brody, who bought it for $17,000 in 1952 from a New York art dealer, who had acquired it from Picasso in 1936. (Sources: Associated Press, "Picasso Painting Fetches World Record $106.5M at NYC Auction," by Ula Ilnytzky, May 4, 2010; Online Associated Newspapers, May 6, 2010)
Assuming that the value A0 of the painting has grown exponentially:
a) Find the value of k, and determine the exponential growth function, assuming A0 = 17,000 and t is the number of years since 1952.
b) Estimate the value of the painting in 2020.
c) What is the doubling time for the value of the painting?
d) After how long will the value of the painting be $240 million, assuming there is no change in the growth rate?