# Math Help - Related Rates Help

1. ## 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.

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.
$\frac{dy}{dt}= \frac{466}{41^2} > 0$
ignore the numbers, just note that $\frac{dy}{dt} > 0$ ... what's that say about cardiac output?