Answer:
89.6 hours
Step-by-step explanation:
Each hour, the initial quantity is multiplied by (1 -0.06)^(1/8), so after t hours, the multiplier is 0.94^(t/8). We want to find the value of t that makes this multiplier equal to 1/2.
0.5 = 0.94^(t/8)
log(0.5) = (t/8)log(0.94) . . . . . . . . take logs
t = 8·log(0.5)/log(0.94) ≈ 89.6 . . . divide by the coefficient of t
The half-life of the substance is 89.6 hours.
