Question

When you breathe normally, about 12% of the air in your lungs is replaced with each breath. Write a function that models the amount of the original air left in your lungs, given that the initial volume of air is 500 ml. Use your model to determine how much of the original 500 ml remains after 50 breaths.

Answer 1

The expression is: air(n) = air(0)*0.88^n

The amount of original air in our lungs after 50 breaths if the initial amount was 500 ml is equal to 0.83775 ml.

Explanation:

Since the original air that was in my lung leaves at a rate of 12%, this means that for each breath the volume of original air in my lung is the prior - 12%, in other words it is the same as 88% from the last breath. Therefore we can create an expression that models this decay by doing the following:

Originally:

air(0) = 500 ml

After the first breath we lose 12%, so:

air(1) = air(0)*0.88

This happens again for the second breath:

air(2) = air(1)*0.88 = air(0)*0.88*0.88 = air(0)*(0.88)²

This will repeat as many times as we breath, therefore the expression that models this decay is:

air(n) = air(0)*0.88^n

Applying the data from the problem, we have:

air(n) = 500*0.88^n

To find out the amount of air after 50 breaths, we need to make n = 50 and solve the equation.

air(50) = 500*0.88^(50) = 500*0.0016755 = 0.83775 ml