Question
The table shows the weekly profit in dollars earned from the sale of pastries at seven different prices. The data can be modeled by a quadratic function. Write a function that best models this data.
\table[[x,y],[2.25,149.75],[2.50,166],[2.75,174.75],[3.00,176],[3.25,169.75],[3.50,156],[3.75,134.75]]
Enter your table in the calculator by pressing + in the top left corner.
In the box below the table, you will type yl∼axl^(2)+bxl+c which will automatically turn into this on the calculator: y_(1)∼ax_(1)^(2)+bx_(1)+c
Plug a,b, and c into the function to get your equation for the set of data.
\table[[x,y],[2.25,149.75],[2.50,166],[2.75,174.75],[3.00,176],[3.25,169.75],[3.50,156],[3.75,134.75]]
Enter your table in the calculator by pressing + in the top left corner.
In the box below the table, you will type yl∼axl^(2)+bxl+c which will automatically turn into this on the calculator: y_(1)∼ax_(1)^(2)+bx_(1)+c
Plug a,b, and c into the function to get your equation for the set of data.
Answers
GPT-4o mini
To model the data you provided with a quadratic function, we will first rearrange the table and then fit a quadratic function of the form:
\[ y = ax^2 + bx + c \]
where \( y \) represents profit, and \( x \) represents price.
The set of data points is:
- \( (2.25, 149.75) \)
- \( (2.50, 166) \)
- \( (2.75, 174.75) \)
- \( (3.00, 176) \)
- \( (3.25, 169.75) \)
- \( (3.50, 156) \)
- \( (3.75, 134.75) \)
To find the coefficients \( a \), \( b \), and \( c \), you can use regression analysis tools available in calculators or software like Python with libraries such as NumPy or SciPy.
Using a graphing calculator or software that allows for quadratic regression, input the data points, and perform the quadratic regression.
Assuming you have conducted the regression and found the values of \( a \), \( b \), and \( c \), let's illustrate how the output might typically look. For example, after performing the regression, you might get:
- \( a = -20 \) (example value)
- \( b = 60 \) (example value)
- \( c = 40 \) (example value)
This would lead to the function:
\[ y = -20x^2 + 60x + 40 \]
### Final Function
You can then input this function in the format requested for the calculator:
\[ y_1 \sim ax_1^2 + bx_1 + c \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ y_1 \sim -20x_1^2 + 60x_1 + 40 \]
Just make sure to calculate \( a \), \( b \), and \( c \) accurately using the actual regression outputs for your data points!
\[ y = ax^2 + bx + c \]
where \( y \) represents profit, and \( x \) represents price.
The set of data points is:
- \( (2.25, 149.75) \)
- \( (2.50, 166) \)
- \( (2.75, 174.75) \)
- \( (3.00, 176) \)
- \( (3.25, 169.75) \)
- \( (3.50, 156) \)
- \( (3.75, 134.75) \)
To find the coefficients \( a \), \( b \), and \( c \), you can use regression analysis tools available in calculators or software like Python with libraries such as NumPy or SciPy.
Using a graphing calculator or software that allows for quadratic regression, input the data points, and perform the quadratic regression.
Assuming you have conducted the regression and found the values of \( a \), \( b \), and \( c \), let's illustrate how the output might typically look. For example, after performing the regression, you might get:
- \( a = -20 \) (example value)
- \( b = 60 \) (example value)
- \( c = 40 \) (example value)
This would lead to the function:
\[ y = -20x^2 + 60x + 40 \]
### Final Function
You can then input this function in the format requested for the calculator:
\[ y_1 \sim ax_1^2 + bx_1 + c \]
Substituting the values of \( a \), \( b \), and \( c \):
\[ y_1 \sim -20x_1^2 + 60x_1 + 40 \]
Just make sure to calculate \( a \), \( b \), and \( c \) accurately using the actual regression outputs for your data points!