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Question:

If the half-life of a radioactive material is 5 years, then what percentage of it remains after 25 years?

3.125

1.25

25

6.25

Solution:

Half-life of material = 5 years = ln2/k, where k is the decay constant.
Amount of material after time t = N(t) = N₀e⁻ᵏᵗ
=> N/N₀ = e⁻⁵ln2 = e⁻ln2⁵ = 0.03125 = 3.125%