Answer:
V(t)=2020+508sin((pi/2)t))
Explanation:
breathing can be seen as an oscillatory function, so it would be perfect to use a sine or cosine function.
for this reason this is an equation of the form
V(t)=C+Asin(Wt)
as we know that there is always a fixed amount of air in the lungs (2020ml) which indicates that it is a constant amount.
on the other hand, the amount of air that moves in the lungs varies between 0l and 508ml for this reason this will be the amplitude
W=2pi/T
the period (T) is defined as the amount of time it takes for a function to repeat itself, in our case it is 4
W=2pi/4=pi/2
considering all of the above
V(t)=2020+508sin((pi/2)t))
Answer:
[tex]v(t) = 2274 + 254 sin(\frac{\pi}{2}t)[/tex]
Explanation:
[tex]V_{min} = 2020 ml[/tex]
[tex]V_{max} = 2020 + 508 =2528 mL[/tex]
Assuming the given function is cyclic function
[tex]v_{avg} = \frac{v_{max} - v_{min}}{2} = \frac{2528 + 2020}{2} = 2274 ml[/tex]
Amplitude [tex]= A = \frac{V_{max} - V_{min}}{2}= \frac{2528 - 2020}{2}= 254[/tex]
time period is 4 sec
we know that [tex]\omega = \frac{2\pi}{t} = \frac{2\pi}{4} = \frac{pi}{2} rad/s[/tex]
so function is
[tex]V(t) = V_{avg} + Asin (\omega t})[/tex]
[tex]v(t) = 2274 + 254 sin(\frac{\pi}{2}t)[/tex]
