Question

the level of fame of an artist is assigned from 1 to 10, with 10 signifying the most famous artist. data are collected about the selling prices for painting and the level of fame of the artists. the model $hat{y}=948.25(2.998)^x$ is calculated, where $x$ represents the artists fame score and $hat{y}$ represents the predicted selling price of the painting. use the model to predict the selling price of a painting whose artists fame is a level 4. $65,316 $76,604 $94,825 $113,714

Explanation:

Step1: Identify the value of x

The artist's fame level $x = 4$.

Step2: Substitute x into the model

We have the model $\hat{y}=948.25(2.998)^x$. Substitute $x = 4$ into it:
$\hat{y}=948.25\times(2.998)^4$.
First, calculate $(2.998)^4=2.998\times2.998\times2.998\times2.998\approx80.77$.
Then, $948.25\times80.77 = 948.25\times(80 + 0.77)=948.25\times80+948.25\times0.77=75860+730.1525 = 76590.1525\approx76604$.

Answer:

$76,604$