- (C) If Q(t) is the amount of contaminant in the tank at time t and Q 0 is the initial amount, then
= kQ and Q(t) = Q 0 ekt.Since Q(1) = 0.8Q 0 , 0.8Q 0 = Q 0 ek · 1, 0.8 = ek, and
Q(t) = Q 0 (0.8)t.
We seek t when Q(t) = 0.02Q 0. Thus,
0.02Q 0 = Q 0 (0.8)t
and
t 17.53 min.