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Math Help - Cost function

  1. #1
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    Cost function

    I'm having issues remembering how to create cost functions:

    For a long-distance phone call, a hotel charges $9.89 for the first minute and $0.90 for each additional minute or fraction thereof. A formula for the cost is given below, where t is the time in minutes

    So the function is ?

    C(t)=9.89-0.90[[-(t-1)]]

    Do I just distribute that out?


    Use a graphing utility to graph the cost function for 0 < t ≤ 5.

    How do I set the paramaters for this requirement to graph this on my calculator ?





    Last edited by Jerry99; August 19th 2012 at 12:40 PM.
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  2. #2
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    Re: Cost function

    Quote Originally Posted by Jerry99 View Post
    I'm having issues remembering how to create cost functions:
    For a long-distance phone call, a hotel charges $9.89 for the first minute and $0.90 for each additional minute or fraction thereof. A formula for the cost is given below, where [I]t is the time in minutes
    So the function is ?
    C(t)=9.89-0.90[[-(t-1)]]
    I would use the ceiling function: C(t) = 9.90 + 0.90\left\lceil {t - 1} \right\rceil
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  3. #3
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    Re: Cost function

    Hello, Jerry99!

    That cost function is scary . . .


    For a long-distance phone call, a hotel charges $9.89 for the first minute
    and $0.90 for each additional minute or fraction thereof.
    A formula for the cost is given below, where t is the time in minutes

    So the function is ?

    C(t) = 9.89 - 0.90[[-(t-1)]] . Weird!


    Use a graphing utility to graph the cost function for 0 < t ≤ 5.

    How do I set the paramaters for this requirement to graph this on my calculator?

    The hotel charges $9.89 for the first minute.
    It charges $0.90 per minute for the other t-1 minutes.
    The "or fraction thereof" means that they will round up when a fraction is involved.
    . . Hence, the remaining time is \lceil t-1\rceil minutes (ceiling function).

    The cost is: . C \:=\:9.89 + 0.90\lceil t-1\rceil


    The graph looks like this.

    Code:
              |
       $13.49 +                       o=====♠
              |                       :     :
              |                       :     :
       $12.59 +                 o=====♠     :
              |                 :     :     :
              |                 :     :     :
       $11.69 +           o=====♠     :     :
              |           :     :     :     :
              |           :     :     :     :
       $10.79 +     o=====♠     :     :     :
              |     :     :     :     :     :
              |     :     :     :     :     :
        $9.89 o=====♠     :     :     :     :
              |     :     :     :     :     :
              |     :     :     :     :     :
              |     :     :     :     :     :
          - - * - - + - - + - - + - - + - - + - -
              0     1     2     3     4     5  minutes
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  4. #4
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    Re: Cost function

    Ok thanks guys
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