The air in a factory is being filtered so that the quantity of a pollutant, P(measured in mg/liter), is?

Question

decreasing according to the equation P = Qe^(-kt), where t represents time in hours. If 10% of the pollution is removed in the first five hours:
(a) What percentage of the pollution is left after 15 hours?
(b) How long will it take before the pollution is reduced to 10%?

Answer 1

This is exponential decay. Time constant = (x1-x2)/(ln(y1)-ln(y2)) = 47.5 hr, where (x1,y1) is initial state (x=0,y=1) and (x2,y2) is next state (x=5,y=0.9).

(a) This can be found by simple exponentiation.
P(5) = 0.9
P(15) = P(5)^(15/5) = 0.9^3 = 0.729

(b) This uses logarithms.
P(t) = 0.9^(t/5)
t = 5*ln(P)/ln(0.9)
For P = 0.1, t = 109.3 hrs.