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Math Help - Functions - PLEASE HELP

  1. #1
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    Functions - PLEASE HELP

    Hi Guys, I need to know how to create a function and graph using the data below. It shows the costs for a school trip to a school.
    20 children = 100
    21 = 95
    22 = 90
    23 = 85
    24 = 80
    25 = 75
    26 = 70
    27 = 65
    28 = 60
    29 = 55
    30 = 150
    31 = 176
    32 = 172
    33 = 168
    34 = 164
    35 = 160
    36 = 156
    37 = 152
    38 = 148
    39 = 144
    40 = 240
    41 = 277
    42 = 274
    43 = 271
    44 = 268
    45 = 265
    46 = 262
    47 = 259
    48 = 256
    49 = 253
    50 = 250

    As you can see the data is quite random. How can I tlk about this data in regards to functions and graphs?

    PLEASE HELP.
    31 = 145
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  2. #2
    Flow Master
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    Quote Originally Posted by Berwick View Post
    Hi Guys, I need to know how to create a function and graph using the data below. It shows the costs for a school trip to a school.
    20 children = 100
    21 = 95
    22 = 90
    23 = 85
    24 = 80
    25 = 75
    26 = 70
    27 = 65
    28 = 60
    29 = 55
    30 = 150
    31 = 176
    32 = 172
    33 = 168
    34 = 164
    35 = 160
    36 = 156
    37 = 152
    38 = 148
    39 = 144
    40 = 240
    41 = 277
    42 = 274
    43 = 271
    44 = 268
    45 = 265
    46 = 262
    47 = 259
    48 = 256
    49 = 253
    50 = 250

    As you can see the data is quite random. How can I tlk about this data in regards to functions and graphs?

    PLEASE HELP.
    31 = 145
    Plot the data as a scatter plot. Then decide on a model to use to fit the data. Then use technology to fit that model to the scatterplot. You might need to investigate several models - use the one that gives the largest value of r (the correlation coefficient). The value of r will be given to you by the technology you use.
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Data and functions

    Hello Berwick

    If, as you say, the data is as random as that - and it seems nonsense that this should be the pattern of costs for a school trip - then you won't find a simple algebraic function to represent all the data.

    But if you break it down into several ranges of values, you can find functions for each range.

    So, suppose n is the number of children going on the trip, and the cost is C. Then in the range 20\le n \ 29, for each 1 that n increases, C decreases by 5. So C will be in the form A - 5n. And when n = 20, C = 100. So A = 200.

    So for 20\le n \le 29, C = 200 - 5n.

    (Note that if there's a typo at n = 30, and it should read C = 50, then you can include n = 30 in this formula as well.)

    In a similar way, if 31 \le n \le 39 (or 40 if there's a similar typo at n = 40), the formula you want is C = 300 - 4n.

    And if 41 \le n \le 50, C = 400 - 3n.

    As far as plotting a graph is concerned, what about using Excel?

    Grandad


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