1.4+Setting+the+Right

AE Big Idea: Many real world situations can be modeled and predicted using mathematics. Essential Question:What are some of the variables around us? Notes:
 * 12/09/08

Problem 1.4 Setting the right price ****A) Graph the (price,buyers) data, and draw a straight line that models the trend in the data.

** ** || **2 ** || **4 ** || **6 ** || **8 ** || **10 ** || **12 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">400 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">325 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">230 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">160 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">100 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">25 ** || <span style="FONT-FAMILY: 'Comic Sans MS', cursive"> <span style="FONT-FAMILY: 'Comic Sans MS', cursive"> <span style="FONT-FAMILY: 'Comic Sans MS', cursive">
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">Price (dollars)
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">Number of buyers


 * <span style="FONT-FAMILY: 'Comic Sans MS', cursive"><span style="FONT-FAMILY: 'Comic Sans MS', cursive">B) Write a linear of the form y=mx+b for your graph model.

y=mx+b (2, 400) x=2.4 y=mx+475(the y-intercept) (4, 325) y=400, 325 __y=37.5x+475__ y2-y/ x2-x= 400-325/ 2-4 =75/ 2 =37.5 My equation was y=37.5x+475. I got this because the slope is 37.5x and the y-intercept is 475.

C)What do the patterns of change in the (price, buyers) data and the graph model tell you about the relationship between the price and the number of buyers?

The patterns of change tell me that as the price decreases the amount of buyers increase, my evidence for this statement is with 12$ per hat only 25 people would be willing to pay, and with 2$ per hat 400 people would be willing to pay.

D)What do the values of //m// and //b// in the equation model tell you about the relationship between the price and the number of buyers?

It tells us that if the price was dropped to 0$ then 475 people would take a baseball cap out of 500 students (500 is the total amount of students). I know this because my graph model crosses the y-axis at 475.

E)Which data pair from the survey data is the furthest away from your graph model?

The farthest co-ordinate is (6,230), this is because its not as close to my grpah model as my other co-ordinates.

2 4 6 8 10 400 --->(75)-->325--->(95)-->230--->(70)-->160--->(60)-->100

Problem 1.4 Follow-up

1)What do the numbers -40 and 480 in the equation tell you about the relationship between the price and the numbers of buyers? What do they tell you about the graph relationship?

The numbers tell me that if the price was 0$ 480 people would take the hat for free but 20 people wouldn't. And the -40 tells me that the line is steeper because it has a steeper slope.

2) Although the SGA gathered data for only a few prices, they can use their equation model to make a table with information for many more prices. a)Make a table. In the second column, enter the number of buyers the equation model y=-40x+480 predicts for each whole-number price from $2 - $15.

** ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">Number of buyers ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">Income (dollars) ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">400 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$800 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">360 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1080 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">320 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1280 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">280 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1400 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">240 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1440 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">200 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1400 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">160 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1280 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">120 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$1080 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">80 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$800 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">40 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$440 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">0 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$0 ** || ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">0 ** || **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$0 ** ||
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">Price (dollars)
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$2
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$3
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$4
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$5
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$6
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$7
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$8
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$9
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$10
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$11
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$12
 * **<span style="FONT-FAMILY: 'Comic Sans MS', cursive">$13
 * <span style="FONT-FAMILY: 'Comic Sans MS', cursive">b) Which data pair from the survey is most different from the prediction made by the equation model? Are any predictions the same as the survey data?

The most different data pair is $12 and 0 number of buyers. For 8$, 160 number of buyers was the only prediction made that was correct.

3)How much should the SGA charge for each cap if they want the maximum possible income?

The SGA should charge 6$ per cap to get the maximum income because 6$ multiplied by the number of of buyers (240)=1440, which is the highest possible income even though less people would buy a hat.

4)Make a graph of the (price, income) data. Describe the shape of your graph. How is your answer to question 3 shown on your graph?

My graph has a curve because of the income pattern. The curves 'peak' is (6$, 1400), so this tells us that the curve bends the other way. **