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

The value of A and B are 0.6 and
`B=(2\pi)/(5)` respectively.

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=(2\pi)/(B)`

`5=(2\pi)/(B)`

`B=(2\pi)/(5)`

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

`f(t)=y =0.6\sin ((2\pit)/(5))`

The value of A and B are 0.6 and
`B=(2\pi)/(5)` respectively.

The graph of is shown below: