The value of a painting recently sold at an auction can be modeled by the function v(t)=12,000(1.15)^t . The exponential function models the relationship between the value of the painting, v(t), in dollars, and the number of years, t, since the painting was sold at the auction.

Question

Which statement correctly interprets this model?
A.
Each year the painting increases its value by 12,000 percent.

B.
The painting was sold at the auction 12,000 years ago.

C.
Each year the painting increases its value by 15 percent.

D.
The painting was sold at the auction 1.15 years ago.

Answer 1

The correct interpretation of the model \( v(t) = 12,000(1.15)^t \) is option C:

C. Each year the painting increases its value by 15 percent.

Here's the reasoning:

• The equation models the value \( v(t) \) of the painting at time \( t \) years after the auction.
• The base of the exponential function, \( 1.15 \), indicates the growth factor. Specifically, \( 1 + \text{growth rate} = 1.15 \) means the painting increases in value by 15% each year. Hence, the correct interpretation is that each year the painting's value increases by 15%.