Question

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation (t = 0) to the end of exhalation takes about t = 5 s. the maximum rate of air flow into the lungs is about 0.3 l/s. this explains, in part, why the function f(t) = 3 10 sin(2t/5) 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

The volume of inhaled air in the lungs can be determined by integrating the given function and evaluating it at the desired time. The resulting expression is then multiplied by the maximum rate of air flow into the lungs to obtain the volume in liters.

Step-by-step explanation:

The volume of inhaled air in the lungs at a given time can be determined using the model f(t) = 3 * 10 * sin(2t/5), where t is the time in seconds. To find the volume of inhaled air, we need to integrate the function from the beginning of inhalation (t = 0) to the desired time (t).

Integrating the function gives us the antiderivative F(t) = -30/5 * cos(2t/5). To find the volume of inhaled air at a specific time t, we need to evaluate F(t) - F(0). This gives us the expression -30/5 * (cos(2t/5) - 1).

To find the volume of inhaled air in liters, we need to multiply the expression by the maximum rate of air flow into the lungs (0.3 l/s). So the volume of inhaled air at time t is -9 * (cos(2t/5) - 1) l.