The value V (in millions of dollars)of a famous painting can be modeled by $V = 10 e ^ {k t }$ where t represents the year,with t = 0 corresponding to 2000.In 2008,the same painting was sold for $65 million.Predict the value of the painting in 2018.(Round your answer to two decimal places. )
A)$674.61 million
B)$874.61 million
C)$474.61 million
D)$774.61 million
E)$574.61 million

Question

The value V (in millions of dollars)of a famous painting can be modeled by $V = 10 e ^ {k t }$ where t represents the year,with t = 0 corresponding to 2000.In 2008,the same painting was sold for $65 million.Predict the value of the painting in 2018.(Round your answer to two decimal places. ) ​
A)$674.61 million
B)$874.61 million
C)$474.61 million
D)$774.61 million
E)$574.61 million

Quizplus · Accepted Answer

To predict the value of the painting in 2018, we first need to find the value of $k$ using the information that in 2008 (t = 8), the painting was sold for $65 million. We substitute these values into the equation $V = 10e^{kt}$ to get $65 = 10e^{8k}$. Solving for $k$, we find $k \approx 0.1845$. Then, to find the value in 2018 (t = 18), we substitute $k$ and $t$ into the original equation to get $V = 10e^{(0.1845)(18)} \approx 674.61$ million dollars.

The Value V (In Millions of Dollars)of a Famous Painting V=10ektV = 10 e ^ {k t }V=10ekt

The Value V (In Millions of Dollars)of a Famous Painting $V = 10 e ^ {k t }$