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: