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Math Help - Related Rates Help

  1. #1
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    Related Rates Help

    The problem+some scientific background:
    Cardiac Output: A normal person's cardiac output is 7 liters a minute. When they're resting it's 6L/min. A marathon's runner cardiac output can be as high as 30L/min. Cardiac Output can be calculated with a formula: y=Q/D.
    Where Q is the number of milliliters of CO2 you exhale in a minute and D is the difference between the CO2 concentration in the blood returning from the lungs. With Q=233mL/min and D=97-56=41 mL/L, y=5.68L/min, which is close to 6L/min (resting position). The Question:
    Suppose that when Q=233 and D=41, we also know that D is decreasing at the rate of 2 units a minute but that Q remains unchanged. What is happening to the cardiac output?

    From what I can see, the cardiac output is getting higher, since the person in the problem is active; since D is decreasing. However I have to show my work, which is the difficult part. I'm guessing I should use the quotient rule on Q/D as D being the variable and Q as a constant. After that I should differentiate it, since I'm finding the change in y. So I'm ending up with:
    Change in Y=((41x0)-(233x-2(read as 233 times -2)))/(41^2)
    I feel like I'm doing something wrong, since to me my answer doesn't really make sense. Any kind of help will be nice, thank you.
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  2. #2
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    Quote Originally Posted by maximade View Post
    The problem+some scientific background:
    Cardiac Output: A normal person's cardiac output is 7 liters a minute. When they're resting it's 6L/min. A marathon's runner cardiac output can be as high as 30L/min. Cardiac Output can be calculated with a formula: y=Q/D.
    Where Q is the number of milliliters of CO2 you exhale in a minute and D is the difference between the CO2 concentration in the blood returning from the lungs. With Q=233mL/min and D=97-56=41 mL/L, y=5.68L/min, which is close to 6L/min (resting position). The Question:
    Suppose that when Q=233 and D=41, we also know that D is decreasing at the rate of 2 units a minute but that Q remains unchanged. What is happening to the cardiac output?

    From what I can see, the cardiac output is getting higher, since the person in the problem is active; since D is decreasing. However I have to show my work, which is the difficult part. I'm guessing I should use the quotient rule on Q/D as D being the variable and Q as a constant. After that I should differentiate it, since I'm finding the change in y. So I'm ending up with:
    Change in Y=((41x0)-(233x-2(read as 233 times -2)))/(41^2)
    I feel like I'm doing something wrong, since to me my answer doesn't really make sense. Any kind of help will be nice, thank you.
    your "answer" makes perfect sense ...

    \frac{dy}{dt}= \frac{466}{41^2} > 0

    ignore the numbers, just note that \frac{dy}{dt} > 0 ... what's that say about cardiac output?
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  3. #3
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    Your answer makes perfect sense, you shouldn't doubt yourself.
    We've completed this problem in class and your answer is correct.
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