A simple model for the flow of air in and out of the lungs of a certain mammal is given by the following equation, where V(t) (measured in liters) is the volume of air in the lungs at time t20, tis measured in seconds, and t=0 corresponds to a time at which the lungs are full and exhalation begins. Only a fraction of the air in the lungs is exchanged with each breath. The amount that is exchanged is called the tidal volume. Complete parts a through c below. V'(t) = -5 sin a. Find the volume function V, assuming that V(0) = 12 L. Notice that V changes over time at a known rate, V'. Which equation below correctly gives the volume function? O A. V(0)= V() + Jv'c) dx. O B. V(0) = V(t) + V'(t)dt. a OC. V(t) = V(0) + V't)dt. O D. V(1) = V(0) + |v'(x) dx. Find the volume function V, assuming that V(0) = 12 L. It V(t) = 11+ cos (Type an exact answer.) b. What is the breathing rate in breaths/minute? The breathing rate is breaths/minute. (Type an integer or a simplified fraction.) c. What is the tidal volume and what is the total capacity of the lungs? The tidal volume is liter(s). (Type an integer or a simplified fraction.) The total capacity of the lungs is liter(s). (Type an integer or a simplified fraction.)

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Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
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A simple model for the flow of air in and out of the lungs of a certain mammal is given by the following equation, where V(t) (measured in liters) is the volume of air in the lungs at time t20, tis measured in seconds, and t=0 corresponds to a time at which the lungs are full and exhalation begins. Only a fraction of the air in the
lungs is exchanged with each breath. The amount that is exchanged is called the tidal volume. Complete parts a through c below.
V'(t) = -5 sin
a. Find the volume function V, assuming that V(0) = 12 L. Notice that V changes over time at a known rate, V'. Which equation below correctly gives the volume function?
O A. V(0)= V() + Jv'c) dx.
O B. V(0) = V(t) +
V'(t)dt.
a
OC. V(t) = V(0) + V't)dt.
O D. V(1) = V(0) + |v'(x) dx.
Find the volume function V, assuming that V(0) = 12 L.
It
V(t) = 11+ cos
(Type an exact answer.)
b. What is the breathing rate in breaths/minute?
The breathing rate is breaths/minute.
(Type an integer or a simplified fraction.)
c. What is the tidal volume and what is the total capacity of the lungs?
The tidal volume is liter(s).
(Type an integer or a simplified fraction.)
The total capacity of the lungs is liter(s).
(Type an integer or a simplified fraction.)
Transcribed Image Text:A simple model for the flow of air in and out of the lungs of a certain mammal is given by the following equation, where V(t) (measured in liters) is the volume of air in the lungs at time t20, tis measured in seconds, and t=0 corresponds to a time at which the lungs are full and exhalation begins. Only a fraction of the air in the lungs is exchanged with each breath. The amount that is exchanged is called the tidal volume. Complete parts a through c below. V'(t) = -5 sin a. Find the volume function V, assuming that V(0) = 12 L. Notice that V changes over time at a known rate, V'. Which equation below correctly gives the volume function? O A. V(0)= V() + Jv'c) dx. O B. V(0) = V(t) + V'(t)dt. a OC. V(t) = V(0) + V't)dt. O D. V(1) = V(0) + |v'(x) dx. Find the volume function V, assuming that V(0) = 12 L. It V(t) = 11+ cos (Type an exact answer.) b. What is the breathing rate in breaths/minute? The breathing rate is breaths/minute. (Type an integer or a simplified fraction.) c. What is the tidal volume and what is the total capacity of the lungs? The tidal volume is liter(s). (Type an integer or a simplified fraction.) The total capacity of the lungs is liter(s). (Type an integer or a simplified fraction.)
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