Question

A 17650 cubic foot room initially has a radon level of 870 picocuries per cubic foot. A ventilation system is installed that brings in 385 cubic feet of air per hour that contains 5 picocuries per cubic foot, while an equal quantity of the well-mixed air in the room leaves the room each hour. Setup and use a differential equation to determine how long it will take for the room to reach a safe to breathe level of 105 picocuries per cubic foot. (Round your answer to 5 decimal places.)

Answer 1

N(0) = 870 *17650
d N/dt = 385 *5 - 385 (N/17650)
dN/dt = 385[5 - (N/17650)]

when does N = 17650(105) ?

say dx/dt = a - k x
try
x = a/k -c e^-kt

here
dN/dt = 1925 - .0218 N
so
k = .0218
a = 1925
and N = 88250 - c e^-.0218 t
when t = 0
e^-.0218 t = 1, use to get c
find when N = 105*17650
CHECK MY ARITHMETIC STEP BY STEP.