Question

The value of a painting recently sold at an auction can be modeled by the function
. The exponential function models the relationship between the value of the painting,
, in dollars, and the number of years,
, since the painting was sold at the auction.

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

To interpret the model correctly, we need to focus on the properties of exponential growth functions, which typically have the form:

\[ V(t) = V_0 \times (1 + r)^t \]

where:
- \( V(t) \) is the value of the painting after \( t \) years,
- \( V_0 \) is the initial value of the painting,
- \( r \) is the growth rate,
- \( t \) is the time in years.

If the growth rate \( r \) is 0.15 (which is 15%), it indicates that the value increases by 15% each year. Therefore, the correct interpretation would be:

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

So, the correct statement is **C**.