Problem $4(15$ points$).$ Two different bacterial species with doubling times of $2h$ and $4h$ are growing in a batch nutrient$-$rich medium with their maximum growth rate. The initial concentrations are the same.

a$.$ What would be the ratio of $\frac{x_1}{x_2}$ after $10h$ of batch growth?

b$.$ How long should the batch growth of the mixed cultures last in order to obtain $\frac{x_1}{x_2}=10?$ Assume exponential growth.