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

question 75

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:

Marginal Benefit

The surplus happiness or utility experienced from using an extra unit of any good or service.

Public Good

A public good is a good that is non-excludable and non-rivalrous, meaning it can be used by everyone freely without depleting its availability to others.

Nonrivalry

A characteristic of certain goods where the consumption by one individual does not reduce availability to others, often seen in digital or public goods.

Nonexcludability

A characteristic of certain goods where it is difficult or impossible to prevent someone from using the good once it has been provided.