Chapter 4.3, Problem 35E

The Most Expensive Artwork to Date 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 $f\left(t\right)=31.87\cdot e^{0.096t}$, where $f\left(t\right)$ 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.