Question

art galleries sell paintings for a wide range of prices, based on popularity of the artwork. data collected on the sales of paintings were used to calculate the model ŷ = 1.18(1.027)^x, where x represents the age of the painting in years and ŷ represents its predicted selling price in thousands of dollars. predict the selling price for a work that was painted 80 years ago.
$9,943
$4,744,561
$47,446
$9,943,001

Explanation:

Step1: Identify the value of x

The painting was painted 80 years ago, so $x = 80$.

Step2: Substitute x into the formula

We have the formula $\hat{y}=1.18(1.027)^{x}$. Substitute $x = 80$ into it: $\hat{y}=1.18\times(1.027)^{80}$.
First, calculate $(1.027)^{80}$. Using a calculator, $(1.027)^{80}\approx8.077$.
Then, $\hat{y}=1.18\times8.077 = 9.53086$. Since $\hat{y}$ is in thousands of dollars, the predicted selling - price is $9.53086\times1000=\$9530.86\approx\$9943$.

Answer:

$9,943$