9514 1404 393
Answer:
- 2.58 half-lives
- 77.5 years
Explanation:
The remaining amount, in terms of t half-lives, is ...
q(t) = 60·(1/2)^t
We want t when q(t) = 10, so ...
10 = 60·(1/2)^t
1/6 = (1/2)^t . . . . . . divide by 60
log(1/6) = t·log(1/2) . . . . take logs
t = log(1/6)/log(1/2) = -0.778151/-0.30103 ≈ 2.58496
It will take about 2.58 half-lives for there to be 10 grams remaining.
In years, that is 2.58×30 = 77.5 years.
