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

question 94

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, $\boldsymbol{C}(\boldsymbol{t})$ is the concentration of the dye in the aorta, and R is measured in liters per minute. Round your answer to one decimal place.
$\begin{array}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|}\hline \boldsymbol{t} & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 & 20 & 22 & 24 \\\hline \boldsymbol{C}(\boldsymbol{t}) & 0 & 0 & 2.6 & 5.9 & 9.7 & 7.9 & 4.6 & 3.5 & 2.2 & 0.8 & 0.2 & 0.1 & 0 \\\hline\end{array}$

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Definitions:

Titin

A large protein found in muscle tissue that plays a role in the elasticity and contraction of muscle.

Isometric Contraction

A type of muscle contraction in which the muscle generates force without changing its length, maintaining a constant length of the muscle.

Isotonic Contraction

A type of muscle contraction in which the muscle changes length while the tension remains constant, enabling movement.

Muscle Fibers

The elongated, narrow cells composing muscles, which can contract to facilitate movement.