Higher: decline after several half-lives

The idea

After n half-lives, the fraction of unstable nuclei left is (1/2)ⁿ. The net decline is the original amount minus what remains. It can be expressed as a ratio of the decline to the initial value: after 2 half-lives, 1/4 is left, so the net decline is 3/4 of the initial value.

1. Find the number of half-lives.
2. Remaining fraction = (1/2)ⁿ.
3. Net decline = 1 − remaining fraction.

Watch out After 3 half-lives, the fraction left is 1/8, not 1/6.