Asphere of polymer of radius r contains an initial amount m_0 of dissolved drug that is uniformly distributed within the sphere initially. if diffusion within the polymer controls the rate of release of the drug to the surrounding environment, then the fractional amount released as a function of time may be written as: m/m_0 = 1 - 6/pi^2 exp (-pi^2 d t/r^2) for 0.5 lessthanorequalto m/m_0 lessthanorequalto 1. a) find an expression for the half-time (i. e. the time at which half of the drug has been released. b) find an expression for the rate of release (dm/dt) at the half-time. this is often used as a nominal measure of the performance of a delivery system. c) what is the characteristic time scale for diffusion in this system? how does the half-time that you calculated in part (a) compare with the estimated characteristic time? is the system in a particular time-dependent limit that we discussed in class, or not necessarily?