Date the fossils

A living thing has a fixed level of carbon-14. After death, half of it is gone every 5730 years. You will write three small functions that turn an age into a fraction and a fraction into an age.

The idea. After $n$ half-lives, a fraction $0.5^n$ of the carbon-14 is left. So the number of half-lives is $\log_2(1 \div \text{fraction})$.

Your tasks.

1. Finish fraction_left. It gives the fraction of the carbon-14 that is left after age years.
2. Finish half_lives. It gives the number of half-lives that have passed when fraction is left.
3. Finish age_of. It gives the age in years of a sample with fraction left.