During normal breathing, about 12% of the air in the lungs is replaced after one breath. Write an exponential decay model for the amount of the original air left in the lungs if the initial amount of air in the lungs is 500 mL. How much of the original air is present after 240 breaths?
after n breaths, the amount left is
500*.88^n
500(0.88)^n
2.370
To model the amount of the original air left in the lungs as a function of the number of breaths, we can use the exponential decay formula:
A(t) = A₀ * e^(-rt)
Where:
A(t) represents the amount of air left in the lungs at time t,
A₀ is the initial amount of air in the lungs,
r is the decay rate, and
t is the time in breaths.
Given that 12% of the air is replaced after one breath, we can calculate the decay rate (r) as follows:
r = ln(1 - 0.12)
Now we can substitute the values into the formula and solve for A(t):
A(t) = 500 * e^(-rt)
To find out how much of the original air is present after 240 breaths, we can substitute t = 240 into the equation:
A(240) = 500 * e^(-r * 240)
To get the answer, we just need to evaluate this expression.