Question

A normal breathing cycle consists of inhaling followed by exhaling. Assume that one complete breathing cycle occurs every 5 seconds, with a maximum airflow rate of 0.6 liters per second. If the function f(t) = A sin Bt is used to model this process, where f(t) gives the airflow at time t, what are the values of A and B?

Answer 1

Answer:

The value of A and B are 0.6 and $B=\frac{2\pi}{5}$ respectively.

Step-by-step explanation:

Consider the provided Information.

It is given that one complete breathing cycle occurs every 5 seconds, with a maximum airflow rate of 0.6 liters per second.

Therefore, period is 5 second and amplitude (A) is 0.6

$period=\frac{2\pi}{B}$

$5=\frac{2\pi}{B}$

$B=\frac{2\pi}{5}$

Substitute the required value in $f(t) = A \sin Bt$

$f(t)=y =0.6\sin (\frac{2\pit}{5})$

The value of A and B are 0.6 and $B=\frac{2\pi}{5}$ respectively.

The graph of is shown below: