To solve this problem, we need to use the given linear model [tex]\( y = 14.2992x - 4.5199 \)[/tex], where [tex]\( y \)[/tex] represents the revenue and [tex]\( x \)[/tex] represents the number of patrons attending. We are asked to predict the revenue when 121 patrons attend.
Here's a step-by-step breakdown:
1. Identify the linear model and the parameters:
- The linear model is given by [tex]\( y = 14.2992x - 4.5199 \)[/tex].
- The slope ([tex]\( m \)[/tex]) is 14.2992.
- The y-intercept ([tex]\( b \)[/tex]) is -4.5199.
2. Substitute the given value of [tex]\( x \)[/tex] (the number of patrons) into the linear model:
- The number of patrons [tex]\( x \)[/tex] is 121.
3. Calculate the revenue [tex]\( y \)[/tex] by substituting [tex]\( x \)[/tex] into the linear equation:
- Substitute [tex]\( x = 121 \)[/tex] into the equation [tex]\( y = 14.2992 \cdot x - 4.5199 \)[/tex]:
[tex]\[
y = 14.2992 \cdot 121 - 4.5199
\][/tex]
4. Evaluate the expression:
- First, multiply the slope by the number of patrons:
[tex]\[
14.2992 \cdot 121 = 1730.2032
\][/tex]
- Then, subtract the y-intercept:
[tex]\[
1730.2032 - 4.5199 = 1725.6833
\][/tex]
5. State the final result:
- Therefore, the revenue predicted for 121 patrons attending is [tex]\( 1725.6833 \)[/tex].
So, the predicted revenue when 121 patrons attend is $1725.68 (rounded to two decimal places).
