Two different bacterial species with doubling times of $2$ h and $4$ h are growing in a batch nutrientrich medium with their maximum growth rate. The initial concentrations are the same.

$($a$)$ What would be the ratio of X$1/$X$2$ after $10$ h of batch growth?

$($b$)$ How long should the batch growth of the mixed cultures last in order to obtain X$1/$X$2=10?$

Assume exponential growth.