Aradioactive material, such as the isotope thorium-234, disintegrates at a rate proportional to the amount currently present. if q(t) is the amount present at time t, then d q/dt = −r q, where r > 0 is the decay rate. a. if 100 mg of thorium-234 decays to 82.04 mg in 1 week, determine the decay rate r. b. find an expression for the amount of thorium-234 present at any time t. c. find the time required for the thorium-234 to decay to onehalf its original amount.