1. The problem statement, all variables and given/known data The radioactive decay of a substance is proportional to the present amount of substance at any time t. If there was 15 grams at t=0 hours and 10 grams at t=3 hours. Set up the differential equation that models this decay and use the method of separation of variables to solve for the equation that will give the amount of the substance at any time t. Find when the half-life occurs and the amount of substance at t=10 hours. 2. Relevant equations 3. The attempt at a solution So I have the equation N = Dekt for the decay Plugging in N = 15 grams at t = 0 gives mt D = 15 Then plugging in t=3 and N = 10 grams 10 = 15e3k I get k = ln(10)/45 The half life occurs at 0.5N 0.5N = 15eln(10)/45 * t Solving for t I get t = (45*7.5)/300 t = 1.125 hours But this doesn't make sense. Was I wrong to assume that N = 7.5 at the half-life time?