í Cardiac output is the rate R of volume of blood pumped by the heart per unit time (in liters per minute). Doctors measure R by inject- ing A mg of dye into a vein leading into the heart at i = 0 and recording the concentration c(t) of dye (in milligrams per liter) pumped out at short regular time intervals (Figure 8). (a) Explain: The quantity of dye pumped out in a small time interval [1,1 + Ar] is approximately Rc(t)At. (b) Show that A = R c(1)dt, where T is large enough that all of the dye is pumped through the heart but not so large that the dye returns by recirculation. (c) Assume A = 5 mg. Estimate R using the following values of c(t) recorded at l-second intervals 2 4 7 8 10 c(t) 0 0.4 2.8 6.5 9.8 8.9 6.1 4 2.3 1.1 Measure concentration Inject dye here here ç1) (mg/liter) Blood flow y = c(t) t (s) FIGURE 8
í Cardiac output is the rate R of volume of blood pumped by the heart per unit time (in liters per minute). Doctors measure R by inject- ing A mg of dye into a vein leading into the heart at i = 0 and recording the concentration c(t) of dye (in milligrams per liter) pumped out at short regular time intervals (Figure 8). (a) Explain: The quantity of dye pumped out in a small time interval [1,1 + Ar] is approximately Rc(t)At. (b) Show that A = R c(1)dt, where T is large enough that all of the dye is pumped through the heart but not so large that the dye returns by recirculation. (c) Assume A = 5 mg. Estimate R using the following values of c(t) recorded at l-second intervals 2 4 7 8 10 c(t) 0 0.4 2.8 6.5 9.8 8.9 6.1 4 2.3 1.1 Measure concentration Inject dye here here ç1) (mg/liter) Blood flow y = c(t) t (s) FIGURE 8
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
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![í Cardiac output is the rate R of volume of blood pumped by the
heart per unit time (in liters per minute). Doctors measure R by inject-
ing A mg of dye into a vein leading into the heart at i = 0 and recording
the concentration c(t) of dye (in milligrams per liter) pumped out at short
regular time intervals (Figure 8).
(a) Explain: The quantity of dye pumped out in a small time interval
[1,1 + Ar] is approximately Rc(t)At.
(b) Show that A = R c(1)dt, where T is large enough that all of the
dye is pumped through the heart but not so large that the dye returns by
recirculation.
(c) Assume A = 5 mg. Estimate R using the following values of c(t)
recorded at l-second intervals
2
4
7
8
10
c(t) 0 0.4
2.8
6.5
9.8
8.9
6.1
4
2.3
1.1
Measure
concentration
Inject dye
here
here
ç1) (mg/liter)
Blood flow
y = c(t)
t (s)
FIGURE 8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fab30c284-e9e0-4766-87eb-80579b67a34a%2F9d1d4985-e84e-4d08-b635-b99534d2a02f%2F5mw7ya_processed.png&w=3840&q=75)
Transcribed Image Text:í Cardiac output is the rate R of volume of blood pumped by the
heart per unit time (in liters per minute). Doctors measure R by inject-
ing A mg of dye into a vein leading into the heart at i = 0 and recording
the concentration c(t) of dye (in milligrams per liter) pumped out at short
regular time intervals (Figure 8).
(a) Explain: The quantity of dye pumped out in a small time interval
[1,1 + Ar] is approximately Rc(t)At.
(b) Show that A = R c(1)dt, where T is large enough that all of the
dye is pumped through the heart but not so large that the dye returns by
recirculation.
(c) Assume A = 5 mg. Estimate R using the following values of c(t)
recorded at l-second intervals
2
4
7
8
10
c(t) 0 0.4
2.8
6.5
9.8
8.9
6.1
4
2.3
1.1
Measure
concentration
Inject dye
here
here
ç1) (mg/liter)
Blood flow
y = c(t)
t (s)
FIGURE 8
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