Estimate the value of the quantity.
-The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was 4.6 mg. Plot the data and connect the data points with a smooth curve. Find the Area under the curve using rectangles. Use this area to estimate the cardiac output. $\begin{array}{c|c}
\begin{array}{c}
\text { Seconds } \
\text { after } \
\text { injection }
\end{array} & \begin{array}{c}
\text { Dye Conc. } \
\text { (adjusted for } \
\text { recirculation) }
\end{array} \
\hline 0 & 0 \
2 & 0.5 \
4 & 1.2 \
6 & 2.3 \
8 & 3.8 \
10 & 4.6 \
12 & 4.5 \
14 & 3.2 \
16 & 1.8 \
18 & 0.5 \
20 & 0
\end{array}$

$\text { Dye concentration (mg/L) }$

A) 285.7 L/min
B) 12.6 L/min
C) 0.1 L/min
D) 6.3 L/min

Question

Estimate the value of the quantity.
-The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was 4.6 mg. Plot the data and connect the data points with a smooth curve. Find the Area under the curve using rectangles. Use this area to estimate the cardiac output. $\begin{array}{c|c}
\begin{array}{c}
\text { Seconds } \
\text { after } \
\text { injection }
\end{array} & \begin{array}{c}
\text { Dye Conc. } \
\text { (adjusted for } \
\text { recirculation) }
\end{array} \
\hline 0 & 0 \
2 & 0.5 \
4 & 1.2 \
6 & 2.3 \
8 & 3.8 \
10 & 4.6 \
12 & 4.5 \
14 & 3.2 \
16 & 1.8 \
18 & 0.5 \
20 & 0
\end{array}$

$\text { Dye concentration (mg/L) }$

A) 285.7 L/min 
B) 12.6 L/min 
C) 0.1 L/min 
D) 6.3 L/min

Quizplus · Accepted Answer

To estimate the cardiac output, we need to calculate the area under the curve using rectangles. We will use the trapezoidal rule to estimate the area in this case.

First, we need to convert the time to minutes:

$\begin{array}{c|c}
\begin{array}{c}
\text { Time (min) } \
\text { after } \
\text { injection }
\end{array} & \begin{array}{c}
\text { Dye Conc. } \
\text { (adjusted for } \
\text { recirculation) }
\end{array} \
\hline 0 & 0 \
0.033 & 0.5 \
0.067 & 1.2 \
0.1 & 2.3 \
0.133 & 3.8 \
0.167 & 4.6 \
0.2 & 4.5 \
0.233 & 3.2 \
0.267 & 1.8 \
0.3 & 0.5 \
0.333 & 0
\end{array}$

Next, we will calculate the area under the curve using the trapezoidal rule. We will use a width of 0.033 minutes for each rectangle:

Area = (0.5 + 1.2)/2 x 0.033 + (1.2 + 2.3)/2 x 0.033 + (2.3 + 3.8)/2 x 0.033 + (3.8 + 4.6)/2 x 0.033 + (4.6 + 4.5)/2 x 0.033 + (4.5 + 3.2)/2 x 0.033 + (3.2 + 1.8)/2 x 0.033 + (1.8 + 0.5)/2 x 0.033 + (0.5 + 0)/2 x 0.033

Area = 0.3738 mg/L x min

Now it's time to calculate the cardiac output. We know that the amount of dye injected was 4.6 mg, and the concentration of the dye was adjusted for recirculation. Therefore, we can use the following equation:

Cardiac output = Amount of dye injected / (Area under the curve x Density of dye x Time elapsed)

Density of the dye used in this case is 1.06 g/mL.

Time elapsed is 0.333 minutes.

Cardiac output = 4.6 mg / (0.3738 mg/L x min x 1.06 g/mL x 0.333 min)

Cardiac output = 6.288 L/min

Therefore, the answer is D) 6.3 L/min.

Estimate the Value of the Quantity Dye concentration (mg/L) \text { Dye concentration (mg/L) } Dye concentration (mg/L)

Estimate the Value of the Quantity $\text { Dye concentration (mg/L) }$