Question

When you breathe normally, about 12% of the air in your lungs is replaced with each breath. Write an explicit

formula for the sequence 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

Amount of the original air left in your lungs after n breaths, a(n) = 0.88ⁿ x 500

Amount of the original air left after 50 breaths = 0.837 ml

Explanation:

Initial volume = 500 ml

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

Let a(n) be the amount of the original air left in your lungs after n breaths.

`\texttt{Amount of the original air left in your lungs after 1 breath =}500-(12)/(100)* 500=0.88^1* 500\$\\\\\texttt{Amount of the original air left in your lungs after 2 breaths =}0.88^2* 500\$\\\\\texttt{Amount of the original air left in your lungs after 3 breaths =}0.88^3* 500\$\\\\\texttt{Amount of the original air left in your lungs after n breaths =}0.88^n* 500\$`

Amount of the original air left in your lungs after n breaths, a(n) = 0.88ⁿ x 500

Now we need to find a(n) when n = 50

a(50) = 0.88⁵⁰ x 500 = 0.837 ml

Amount of the original air left after 50 breaths = 0.837 ml

Amount of the original air left after 50 breaths = 0.837 ml