When a person is breathing normally the amount of air in their lawns varies sinusoidally. When full Karen’s lungs hold 2.8 L of air when empty her Lawrence hold 0.6 L of air her brother starts timing her breathing at T equals two seconds she has exhaled completely and at T equals five seconds she has completely inhaled. Create an equation for this

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shallomisaiah19 shallomisaiah19 · Answer 1 · 2020-05-15T03:50:59+02:00

Answer:

[tex]A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6[/tex]

Step-by-step explanation:

Let the function of quantity in the lung of air be A(t)

So [tex]A(t) \alpha \sin (\frac{t - \alpha }{k} )[/tex]

so, A(t) = Amax sin t + b

A(t) = 2.8t⇒ max

A(t) = 0.6t ⇒ min

max value of A(t) occur when sin(t) = 1

and min value of A(t) = 0

So b = 0.6

and A(max) = 2.2

[tex]A(t) = 2.2\sin \frac{(t)}{k} + 0.6[/tex]

at t = 2 sec volume of a is 0.6

So function reduce to

[tex]A(t) = 2.2\sin \frac{(t - 2)}{k} + 0.6[/tex]

and t = 5 max value of volume is represent

so,

[tex]\sin \frac{t - \alpha }{k} = 1[/tex]

[tex]\frac{t - 2}{k} = \frac{\pi }{2}[/tex] when t = 5

[tex]\frac{6}{\pi } = k[/tex]

so the equation becomes

[tex]A(t) = 2.2\sin \frac{(t - 2)\pi }{6} + 0.6[/tex]