Need help finding the missing values and how to solve.

Question

The value V (in millions of dollars) of a famous painting can be modeled by the equation V = 10ekt, where t represents the year, with t = 0 corresponding to 1975. In 2002, the same painting was sold for $20 million. Find the value of k. (Round your answer to four decimal places.)
k =


Use the value of k to predict the value of the painting in 2012. (Round your answer to two decimal places.)
V = $
million

Answer 1

V(t) = 10e^kt

 

In 2002, t = 2002 - 1975 = 27:

 

V(27) = 10e^27k

20 = 10e^27k

2 = e^27k

ln(2) = 27k

ln(2)/27 = k

 

This is the exact answer.  If you want an approximate answer, use your calculator to compute the value of ln(2)/27.