Question

During normal breathing, approximately 11% of the air in the lungs is replaced with each breath. Write an exponential decay model for the amount of original air left in the lungs if the initial amount is 550 milliliters. Calculate the amount of air left after 30 breaths.

a) a = 550 * (0.89)^x
b) a = 550 * (1.11)^x
c) a = 550 * (0.11)^x
d) a = 550 * (0.89)^30

Answer 1

The correct exponential decay model for the amount of original air left in the lungs is a = 550 * (0.89)^x, and after 30 breaths, the calculation would be a = 550 * (0.89)^30.

Step-by-step explanation:

The exponential decay model for the amount of original air left in the lungs, given an initial amount of 550 milliliters and a replacement rate of 11% with each breath, is represented by option (a), which is a = 550 * (0.89)^x. The reason for this is that if 11% of the air is replaced, then 89% of the original air remains after one breath. Therefore, the exponent x indicates the number of breaths taken.

To calculate the amount of air left after 30 breaths, we use the model with x = 30:
a = 550 * (0.89)^30. Executing this calculation provides the amount of original air still in the lungs after 30 breaths.