How would you work these out???

Question

A bottle of wine, which was analyzed for its tritium (3H) content, was found to contain 3.20% of the tritium that was originally present when the wine was bottled. How old (in years) is the bottle of wine? (The half-life of tritium is 12.3 yr.)


and



The half-life of 131I is 8.10 day.
Calculate how much time it would take for an isolated quantity of 131I to decay by 23%.

Answer 1

I will help you on the top problem and you solve the bottom problem yourself.

Use Algebra!
Let the bottle of wine be T years old. Hence follow what given:
3.20% = 2^(-T/12.3)
Take logarithm (base 2) of both side we have:
log(0.0320) = -T/12.3
Hence T = -12.3 * log(0.0320) = 61.1 (years)