Two polymers, $($A and B$)$ containing different amounts of ester groups are to be evaluated for their hydrolytic degradation by surface erosion or drug release. The kinetic constants of degradation for polymer A and B are $0\mathrm{.}001m\frac{g}{m}in$ and $0\mathrm{.}002m\frac{g}{m}in$ respectively. In these materials, the rate of bond cleavage is faster than rate of water diffusion into their bulk and therefore in aqueous environments, drug$-$loaded hydrophobic polymers will release their drug stores independent of water diffusion into their bulk. Their release rates will depend on removal of surface material of the polymer $($surface erosion$)$ and will be proportional to their mass loss. The mass loss over time is given as the first order differential equation below, where $M$ is mass of the polymer at any given time $t$ and $k$ is the kinetic constant of degradation.

$\frac{dM}{dt}=-k$

Solve for the Mass loss, $M.$

How much drug would have been released from polymer A after $60$ minutes if its initial mass was $10mg.$

How much drug would have been released from polymer B after $60$ minutes if its initial mass was $10mg.$

Compare the amounts of drug released by polymers A and $B.$