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# NB TV Size Problem 16

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### NB TV Size Problem 16 - Page Text Content

BC: Why do you suppose the price goes up as the size gets very small? | The main reason for the price going up for very small TVs is probably the portability of the smaller screen. The video resolution is higher and it makes usually for a nicer clearer picture. Portable televisions are good for long car trips or camping trips or can be in ridiculous areas such as the bathroom to show wealth. Also the people think compact technology and smaller high tech equipment is cool and a must have . | size Price Large ......... Smaller........... Very Small.........

FC: Nice TVs Fair Prices by Nate Biedak

1: Question 16: The following are prices of a popular brand of TV Size(inches) Price 5'' \$450 9'' \$430 12'' \$400 15'' \$450 17'' \$510 19'' \$570 21'' \$700 Assume that the price varies quadratically with screen size. Use the ordered pairs of 9'', 15'' and 19'' screens to derive the equation of this function If the manufacturer produced a 24'' TV set, how much would you expect to pay? Use the equation to calculate the prices of 5'' , 12'', 17'', and 21'' diagonal sets Would you describe the quadratic model as accurate, reasonable, or inaccurate? support your answer. Why do you suppose the price goes up as the size gets very small?

2: Assume that the price varies quadratically with screen size. Use the ordered pairs of 9'', 15'' and 19'' screens to derive the equation of this function. | the equation for a quadratic equation is ax^(2 )+bx+c=y so the equation is y=2.67x^2-60.67x+760 go to STAT edit and fill in the columns like this below L1 L2 9 430 15 450 19 570 To find the quadratic equation go back to STAT and over to CALC go down to number 5 which is QuadReg hit enter and it will give you all what is needed to get the equation which is above This is how you find the graph go to the main page on your calculator go to STAT then over to CALC down 5 to QuadReg hit enter and it will appear on your home screen. Now hit 2nd 1 which is L1 hit comma , then 2nd 2 or L2 then comma , then to VARS over to Y-VARS down to Function and hit enter on Y1. Now if you go to Y1 the equation will be there and the parabola on the graph will show

3: If the manufacturer produced a 24'' TV set, how much would you expect to pay? | This is easy to find, the calculator has done all the work for you! Go to Y= then to 2nd graph so the table shows , then go down on the left side until X=24. Then over to the right of that it shows what Y would be or the price so the answer is \$840 | x y 24 840 This is what you should see when you go to the table in your calculator.

4: Use the equation to calculate the prices of 5'' , 12'', 17'', and 21'' diagonal sets | go back to the table and go down to 5 then 12 then 17 then 21 on the left column so... when x=5 y=\$523.33 when x=12 y=416 when x=17 y=499.33 and when in the left column x=21 and y=662 x y 5 523.33 12 416 17 499.33 21 662

5: Would you describe the quadratic model as accurate, reasonable, or inaccurate? support your answer. | This graph only using the three given points is reasonable. Some points are close but others are off. Like in the given chart it says for a 21 inch TV the price would be 700 but in the table or on the graph it will say 662. If you want the graph to be more accurate then all 7 and there corresponding y = numbers should have been plugged into the STAT area(L1 , L2). However the inverted parabola does hit the three given points right on the dot so this is why the graph can be viewed as reasonable and not inaccurate. | Reasonable

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