1. The problem statement, all variables and given/known data A certain nuclear plant produces radioactive waste in the form of strontium-90 at the constant rate of 500kg. The waste decays exponentially with a half-life of 28 years. How much of this radioactive waste from the nuclear plant will be present after the following increments of time? Assume that initially 600kg of strontium-90 is in the nuclear plant. a. N years b. 140 years c. To perpetuity 2. Relevant equations - 3. The attempt at a solution I found that the "rate in" was 500kg/year, and i'm not sure about the "rate out" (rate of depletion of the sample). We are given that the sample decays exponentially, so we should have that y(t) = yo e-0.02475t. We can assume that yo is just y (the radioactive sample that is decaying). Then, the rate of depletion would be (I doubt that this is true): y'(t) = -0.2475ye-0.02475t This is because this is the rate of change of the sample. Then, i set up my differential equation to be the following (k is just the constant k = (ln2)/(half life)): dm/dt = 500 - kme-kt I rearranged the terms into the form dm/dt - P(x)y = f(t), i came up that the integrating factor was actually e-e^(-kt)), but this is not true (while differentiating the function I realized that it it was a completely new expression that was different to the one shown). How can I proceed from this information or have i made a wrong set-up to the exercise? Thank you.