A half-life calculator

You will write four small functions for first order reactions and a pseudo first order test: the half-life, the fraction left, the time to reach a given fraction, and the true rate constant.

The idea. For a first order reaction, $t_{1/2} = \dfrac{0.693}{k}$ and the fraction left after a time $t$ is $\left(\tfrac{1}{2}\right)^{t/t_{1/2}}$. In a pseudo first order reaction, $k' = k[\text{B}]_0$.

Your tasks.

1. Complete half_life(k) so that it returns $t_{1/2}$, using math.log(2) for $\ln 2$.
2. Complete fraction_left(t, t_half) so that it returns the fraction of the reactant left after time $t$.
3. Complete time_to_fraction(left, t_half) so that it returns the time for the fraction left to remain.
4. Complete true_k(k_prime, excess) so that it returns the true rate constant of a pseudo first order reaction.