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Math Help - Modelling and Problem Solving Question

  1. #1
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    Modelling and Problem Solving Question

    Hello,
    I've been trying to solve this problem for a while, and it's really getting to me. We're supposed to use Microsoft Excel, but I don't know where to start with the problem. It is as follows:

    When the kidneys eliminate a chemical from the blood, they tend to eliminate a certain proportion each time period. For example, the average person eliminates about 13% of the caffeine in his or her body each hour. In doses larger than 20mg, caffeine can act as a mild stimulant (it can be toxic in large doses). Assume that a 375mL can of Cola has about 45mg of caffeine.
    Suppose that you have a can of Cola on the hour for three hours. If you had your last Cola at 10 p.m, when can you expect the caffeine that you have ingested to stop having its effect?

    I'm probably making some silly assumptions, but I'm not sure how to start. Thank you.
    Last edited by LawfulSarcastic; May 22nd 2010 at 11:23 PM. Reason: Typo
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  2. #2
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    What does "Suppose that you have a can of Cola on the four for three hours" mean???
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  3. #3
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    Sorry, I was typing it quickly:
    Suppose that you have a can of Cola on the hour for three hours. If you had your last Cola at 10 p.m, when can you expect the caffeine that you have ingested to stop having its effect?
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  4. #4
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    Quote Originally Posted by LawfulSarcastic View Post
    Hello,
    I've been trying to solve this problem for a while, and it's really getting to me. We're supposed to use Microsoft Excel, but I don't know where to start with the problem. It is as follows:

    When the kidneys eliminate a chemical from the blood, they tend to eliminate a certain proportion each time period. For example, the average person eliminates about 13% of the caffeine in his or her body each hour.
    So, letting C(t) be the amount of caffeine in your body t hours after ingesting it, \frac{dC}{dt}= -.13C

    In doses larger than 20mg, caffeine can act as a mild stimulant (it can be toxic in large doses). Assume that a 375mL can of Cola has about 45mg of caffeine.
    Suppose that you have a can of Cola on the hour for three hours. If you had your last Cola at 10 p.m, when can you expect the caffeine that you have ingested to stop having its effect?
    Taking t= 0 when you drink the first can, C1(0)= 45. Solve \frac{dC1}{dt}= -.13C with C1(0)= 45, then find C1(1) when you drink the next can of cola. (Integrate \frac{dC1}{C1}= -.13dt.)

    At this point, \frac{dC2}{dt}= -.13C2 and C2(0)= C1(1) (I have "reset" the clock so the time at drinking the second cola is the new t= 0). Solve for C2 and find C2(1).

    Finally solve \frac{dC3}{dt}= -.13C3 with C3(0)= C2(1).
    Find t such that C3(t)= 25. Remember that this "t" is in hours after 10:00 PM, the time you had the last cola.

    I'm probably making some silly assumptions, but I'm not sure how to start. Thank you.
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