Question

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 3 s. The maximum rate of air flow into the lungs is about 0.6 L/s. This explains, in part, why the function f(t) = 3/5 sin(2t/3) has often been used to model the rate of air flow into the lungs. Use this model to find the volume of inhaled air in the lungs at time t.

Answer 1

To find the volume of inhaled air in the lungs at time t using the given model f(t) = 3/5 sin(2t/3), we can integrate the model function and evaluate it at the desired time values.

Step-by-step explanation:

To find the volume of inhaled air in the lungs at time t using the given model f(t) = 3/5 sin(2t/3), we need to integrate the model function over the desired time interval (t1, t2).

1. First, we need to understand that the integral of the sine function is the negative cosine function. So, the integral of f(t) = 3/5 sin(2t/3) is [(-3/5)(3/2)cos(2t/3)] + C, where C is the constant of integration.
2. Next, we need to replace t2 and t1 in the integral expression with the desired time values.
3. Finally, we can evaluate the integral expression at t2 and subtract it from the evaluation at t1 to find the volume of inhaled air in the lungs between time t1 and t2.

For example, if we want to find the volume of inhaled air in the lungs between t1 = 0 and t2 = 3 seconds, we can use the formula [(-3/5)(3/2)cos(2t/3)] + C and evaluate it at t2 and subtract the evaluation at t1.