Eight Milligrams of a Dye Are Injected into a Vein $n = 12$

question 112

Short Answer

Eight milligrams of a dye are injected into a vein leading the an individual's heart. The concentration of dye in the aorta (in milligrams per liter) measured at 2-sec intervals is shown in the accompanying table. Use Simpson's Rule with $n = 12$ and the formula
$$R = \frac { 60 D } { \int _ { 0 } ^ { 24 } C ( t ) d t }$$ to estimate the person's cardiac output, where $D$ is the quantity of dye injected in milligrams, $C ( t )$ is the concentration of the dye in the aorta, and $R$ is measured in liters per minute. Round to one decimal place.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \boldsymbol{t} & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 \\\hline \boldsymbol{C}(\boldsymbol{t}) & 0 & 0 & 2.6 & 6.3 & 9.7 & 7.5 & 4.5 & 3.5 & 2.2 & 0.6 & 0.3 & 0.1 & 0 \\\hline\end{array}$

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Definitions:

Home-Bound Patient

An individual whose health conditions limit their ability to leave their home for medical care or personal needs.

Intravenous Therapy

Medical treatment involving the delivery of fluids, medications, or nutrients directly into a vein.

Prospective Payment Systems

A healthcare payment method where the amount paid is agreed upon in advance based on the condition being treated rather than the services used.

Professional Standards

Established norms and criteria in a given profession that guide ethical and effective practice.