Respuesta :
Answer:
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
Step-by-step 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.
[tex]\texttt{Amount of the original air left in your lungs after 1 breath =}500-\frac{12}{100}\times 500=0.88^1\times 500\$\\\\\texttt{Amount of the original air left in your lungs after 2 breaths =}0.88^2\times 500\$\\\\\texttt{Amount of the original air left in your lungs after 3 breaths =}0.88^3\times 500\$\\\\\texttt{Amount of the original air left in your lungs after n breaths =}0.88^n\times 500\$[/tex]
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
