A painting was sold in 1985 for $ 1 million. The painting was then resold in 1996 for $10 million.

Question

A painting was sold in 1985 for $ 1 million. The painting was then resold in 1996 for $ 10 million. Assume that the painting's value increases exponentially. Find the exponential growth rate k, and determine the exponential growth function, assuming V₀ = 1. (Round decimals to three places.)

A. k = 0.192; V(t) = 1e^0.192t, where V(t) is in millions and t is the number of years after 1985.

B. k = 0.209; V(t) = 1e^0.209t, where V(t) is in millions and t is the number of years after 1985.

C. k = 0.209; V(t) = 1e^0.209, where V(t) is in millions and t is the number of years after 1985.

D. k = 0.209; V(t) = 1e^0.209t, where V(t) is in millions and t is the number of years after 1997.

Answer 1

10 = e^11k

10 million from 1 million in 11 years at k annual growth rate

take natural logs of both sides

ln10 = 11k

k = ln10/11 = about .20933

=20.933% annual rate of increase

A and D are incorrect

C left out the t in the exponent

B is correct