The radioactive waste from a nuclear reactor has a half-life of 1000 years. Waste is continually produced at the rate of 5 tons per year and stored in a dump site.
(a) Set up an inhomogeneous differential equation, of the form in Exercise 8.1.7, to model the amount of radioactive waste.
(b) Determine whether the amount of radioactive material at the dump increases indefinitely, decreases to zero, or eventually stabilizes at some fixed amount.
(c) Starting with a brand new site, how long will it be until the dump contains 100 tons of radioactive material?