Answer:
10.7 years
Step-by-step explanation:
The decay equation can be written as ...
remaining = initial × (1/2)^(t/(half-life))
Filling in the given values, we can solve for t.
0.100 = 1.35 × (1/2)^(t/2.86)
0.100/1.35 = (1/2)^(t/2.86) divide by 1.35
Taking logs transforms this to a linear equation:
log(0.100/1.35) = (t/2.86)log(1/2)
Since log(a/b) = -log(b/a), we can multiply both sides by -1 and simplify the logs a bit.
log(1.35/.1) = t·(log(2)/2.86)
2.86·log(13.5)/log(2) = t ≈ 10.7 . . . . years
The decay time is about 10.7 years.
