PLEASE answer all questions OR answer 10-20 The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300 What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar? Do any data values seem unusual? Yes or No (circle one) Why? Which quantities do the independent and dependent variables represent? Independent variable: Dependent variable: Draw the scatterplot of the data. Sketch the graph below. Label both axes with what each represents as well as a numerical scale. Does the relationship look linear or quadratic? Using your graphing calculator, find the model (equation) that represents the line or curve of best fit. Write it here. Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model. Does the curve look like a good model? Circle one: Yes or No Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work. Profit: ____________________ Circle one: Extrapolation or Interpolation Does this prediction make sense? Yes or No Why or Why not? Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work. Profit: ____________________ Circle one: Extrapolation or Interpolation Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work. Price: ____________________ Profit: ____________________

PLEASE answer all questions OR answer 10-20 The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300 What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar? Do any data values seem unusual? Yes or No (circle one) Why? Which quantities do the independent and dependent variables represent? Independent variable: Dependent variable: Draw the scatterplot of the data. Sketch the graph below. Label both axes with what each represents as well as a numerical scale. Does the relationship look linear or quadratic? Using your graphing calculator, find the model (equation) that represents the line or curve of best fit. Write it here. Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model. Does the curve look like a good model? Circle one: Yes or No Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work. Profit: Circle one: Extrapolation or Interpolation Does this prediction make sense? Yes or No Why or Why not? Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work. Profit: Circle one: Extrapolation or Interpolation Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work. Price: Profit:

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 81E

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Question

PLEASE answer all questions OR answer 10-20

The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below.

Price	0.00	0.45	0.60	0.75	1.00	1.25	1.40	1.50
Profit	0.00	$720	$900	$990	$845	$625	$560	$300

What factors might influence how much is to be made from the candy sale? Give at least two.
What happens to the profit as the price of each candy bar increases Explain possible reasons for your observations.
How do you suppose the other bands determined the price at which to sell each candy bar?
Do any data values seem unusual? Yes or No (circle one) Why?
Which quantities do the independent and dependent variables represent?
Independent variable: Dependent variable:
Draw the scatterplot of the data. Sketch the graph below. Label both axes with what each represents as well as a numerical scale.
Does the relationship look linear or quadratic?
Using your graphing calculator, find the model (equation) that represents the line or curve of best fit. Write it here.
Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model.
Does the curve look like a good model? Circle one: Yes or No
Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work.
Profit: ____________________
Circle one: Extrapolation or Interpolation
Does this prediction make sense? Yes or No Why or Why not?
Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work.
Profit: ____________________
Circle one: Extrapolation or Interpolation
Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work.
Price: ____________________ Profit: ____________________

Expert Solution

Step 1: Q10)

Q10) .

Equation of best fit quadratic curve = -1373.8x² + 2266.2x + 4.9755

vertex : (0.8348, 939.548)

x-intercepts: (-0.0022,0) and (1.6518,0)

y-intercept: (0,4.976)

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