The highest price ever paid for an artwork at auction was for Pablo Picasso’s 1955 painting Les femmes d’Alger, which fetched $179.4 million in a Christie’s auction in 2015. The painting was last sold in 1997 for $31.9 million. If the painting keeps on appreciating at its current rate, then a model for its value is given by f (t) = 31.87e^0.096t, where f (t) is in millions of dollars and t is the number of years since 1997.

(a) Verify that this function gives an approximation of the value of the painting in 2015.

(b) At what rate is the painting appreciating in 2015?

(c) Estimate the value of the painting in 2020 and the rate at which it is appreciating.