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

question 48

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 $\mathrm { mg } / \mathrm { L }$ , is modeled by
$$c ( t ) = \frac { 1 } { 2 } t ( 15 - t ) , 0 \leq t \leq 15$$
where $t$ is measured in seconds.

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

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Definitions:

Average Total Cost

The total cost of production divided by the number of units produced, representing the average cost per unit.

Marginal Cost

The uptick in complete expenditure resulting from the creation of one more unit of a product or service.

AFC Curve

The average fixed cost curve, representing the fixed costs associated with producing goods or services, spread out over the quantity produced.

Fixed Cost

Costs that do not vary with the level of output or business activity, such as rent, salaries, and insurance premiums.