The volume V, in liters, of air in the lungs during a four-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 − 0.0374t3, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle. (Round your answer to four decimal places.)

It was stated that the respiratory cycle takes 4 seconds. So, you just have to simply substitute t=4 to the equation to find the average volume of air in the lungs per cycle.

[tex]V =0.1729t+ 0.1522t^{2} -0.0374 t^{3} [/tex]

[tex]V =0.1729(4)+ 0.1522(4^{2}) -0.0374 (4^{3} )[/tex]

V = 0.7332 liters of air in one cycle

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-02-04T07:52:22+01:00

A mathematical model is the model which is used to explain the any system and estimate the functions of systems.

The value of the volume of air in the lungs during one cycle is 0.7332 liters.

What is mathematical model?

A mathematical model is the model which is used to explain the any system, the effect of the components by study and estimate the functions of systems.

Given information-

Air in the lungs during a four-second respiratory cycle is given by the model(approx.) as,

[tex]V = 0.1729t + 0.1522 t^2 - 0.0374t^3[/tex]

Here, [tex]V[/tex] is the volume in liters and [tex]t[/tex] is the time in seconds.

As the model given for the respiratory cycle is for the 4 seconds. Thus,

[tex]t=4[/tex]

Put the value of [tex]t[/tex] in the model equation given in the problem. We get,

[tex]V = 0.1729t + 0.1522 t^2 - 0.0374t^3[/tex]

[tex]V = 0.1729\times4 + 0.1522 \times(4^2) - 0.0374\times(3^3)[/tex]

[tex]V=0.6916+2.4352-2.3936\\V=0.7332[/tex]

Hence the value of the volume of air in the lungs during one cycle is 0.7332 liters.

Learn more about the mathematical model here;

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