When you breathe normally, about 12% of the air in your lungs is replaced with each

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.

Step-by-step 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

its is actually 4

Step-by-step explanation: