In 1909, the Pittsburgh Pirates shortstop Honus Wagner forced the American Tobacco Company to withdraw his baseball card that was packaged with cigarettes. Fewer than 60 of the Wagner cards still exist. In 1971, a Wagner card sold for $1000; and in September 2007, a card in near-mint condition was purchased for a record $2.8 million (Source: USA Today, 9/6/07; Kathy Willens / AP).

Assuming that the value W0 of the baseball card has grown exponentially:
a) Find the value of k, and determine the exponential growth function, assuming W0 = 1000 and t is the number of years since 1971.
b) Estimate the value of the Wagner card in 2011.
c) What is the doubling time for the value of the card?
d) After how long will the value of the Wagner card be $10.8 million, assuming there is no change in the growth rate?

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