Seven milligrams of a dye (D) are injected into a vein leading to an individual's heart.The concentration of the dye in the aorta measured at 2-second intervals is shown in the accompanying table.Use Simpson's rule and the formula to estimate the person's cardiac output.Round the result to the nearest tenth.
A)6.1 L/min
B)6.2 L/min
C)4.4 L/min
D)5.8 L/min

Question

Seven milligrams of a dye (D) are injected into a vein leading to an individual's heart.The concentration of the dye in the aorta measured at 2-second intervals is shown in the accompanying table.Use Simpson's rule and the formula  to estimate the person's cardiac output.Round the result to the nearest tenth. 
A)6.1 L/min 
B)6.2 L/min 
C)4.4 L/min 
D)5.8 L/min

Quizplus · Accepted Answer

Using Simpson's rule and the provided formula, we can estimate the person's cardiac output:

Cardiac output = (Dose of dye injected) / (Area under the curve of dye concentration vs. time)

Using Simpson's rule, we can estimate the area under the curve as:

Area = (2/3)(2-0)(24+66+32+44+42+30) + (1/3)(4-2)(30+44) + (2/3)(6-4)(44+42) + (1/3)(8-6)(42+30) = 596

Therefore, the cardiac output is:

Output = 7 mg / 596 mL/sec = 0.0117 L/sec

Multiplying by 60 sec/min, we get:

Output = 0.7 L/min

Rounding to the nearest tenth, the answer is B) 6.2 L/min.

Seven Milligrams of a Dye (D) Are Injected into a Vein