Dye Dilution Is a Method of Measuring Cardiac Output $A \mathrm { mg }$

question 21

Multiple Choice

Dye dilution is a method of measuring cardiac output. If $A \mathrm { mg }$ of dye is used and $c ( t )$ is the concentration of the dye at time $t$ , then the cardiac output over the time interval $[ 0 , T ]$ is given by $F = \frac { A } { \int _ { 0 } ^ { T } c ( t ) d t }$ Find the cardiac output over the time interval $( 0,15 )$ if the dye dilution method is used with $10 \mathrm { mg }$ of dye and the dye concentration, in mg/L, is modeled by
$c ( t ) = \frac { 1 } { 2 } t ( 15 - t ) , 0 \leq t \leq 15$
where $t$ is measured in seconds.

• A) \(0.029\)
• B) \(0.039\)
• C) \(0.026\)
• D) \(0.044\)
• E) \(0.036\)
• F) \(0.020\)

---

Definitions:

Acidity

A measure of the concentration of hydrogen ions in a solution, reflecting its ability to donate protons and determining its pH level.

Alkalinity

the measure of the capacity of water or a solution to neutralize acids, often indicated by its pH level.

Concentration

In chemistry, the measure of the amount of a given substance contained in a unit volume of a liquid or solid material.

Dissolved

The process by which a solid becomes incorporated into a liquid to form a solution.