An office contains $1000 \mathrm { ft } ^ { 3 }$ of air initially free of carbon monoxide. Starting at time $= 0$, cigarette smoke containing $4 \%$ carbon monoxide is blown into the room at the rate of $0.5 \mathrm { ft } ^ { 3 } / \mathrm { min }$. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of $0.5 \mathrm { ft } ^ { 3 } / \mathrm { min }$. Find the time when the concentration of carbon monoxide reaches $0.01 \%$.
A) 8.01 min
B) 6.01 min
C) 5.01 min
D) 7.01 min

Question

Quizplus · Accepted Answer

The concentration of carbon monoxide in the room increases according to the formula $C(t) = \frac{0.02t}{200+t}$, where $C(t)$ is the concentration at time $t$ in percent. Setting $C(t) = 0.01\%$ and solving for $t$ gives $t = 5.01$ minutes.

An Office Contains 1000ft31000 \mathrm { ft } ^ { 3 }1000ft3

An Office Contains $1000 \mathrm { ft } ^ { 3 }$