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Math Help - Linear Equation

  1. #1
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    Linear Equation

    Pharmacological products must specify recommended dosages for adults and children. Two formulas for modification of adult dosages levels for young children are

    Cowling's rule: y = (1 / 24) (t + 1)a
    Friend's rule: y = (2 / 25)ta

    where a denotes the adult dose (in milligrams) and t denotes the age of the child (in years).

    (a) If a = 100, graph the two linear equations on the same axes for 0 <= t <= 12.

    (b) For what age do the two formulas specify the same dosage?
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  2. #2
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    Re: Linear Equation

    Well have you graphed the functions yet?
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  3. #3
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    Re: Linear Equation

    I got 2 parallel Lines.

    First Equation
    t 0 1 2
    y 25/6 25/3 25/2

    Second Equation
    t 0 1 2
    y 0 8 16
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  4. #4
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    Re: Linear Equation

    Hi

    I would tackle the graph plotting by taking t = 0 and t = 12 and calculate the yc and yf values as below -

    t : 0 12
    yc : 25/6 25.13/6 (this is < 72 so these lines must cross)
    yf : 0 72

    I don't think these are actually parallel although they may look so over a smaller range.

    Regards
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  5. #5
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    Re: Linear Equation

    Quote Originally Posted by joshuaa View Post
    I got 2 parallel Lines.

    First Equation
    t 0 1 2
    y 25/6 25/3 25/2

    Second Equation
    t 0 1 2
    y 0 8 16
    $a=100$

    $y_c(t)=y_f(t)$

    $\dfrac {100(t+1)}{24}=\dfrac{200 t}{25}$

    $2500(t+1)=4800t$

    $2500=2300t$

    $t=\dfrac {25}{23}$

    not really that big a deal
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  6. #6
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    Re: Linear Equation

    Thank You. It was helpful.

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