Y2

Polonium is a very dangerous radioactive substance with a half-life of 7.9 months and must be stored (the radioactive mass decreases with time). The new warehouse of (brother of authorizes the storage of 38 tons there per month. We want to model the quantity Q(t) polonium in tons t months after the opening of the warehouse. Upon opening, there is no polonium in the warehouse. Here the rate of change in the quantity of polonium decreases in proportion to the quantity present plus the monthly rate of storage. However, the warehouse can safely hold 245 tonnes of polonium or less. Otherwise the warehouse may explode. Explain why the warehouse will be in danger if the warehouse allows 38 tons of polonium to be stored each month. Calculate the minimum number of tons that the warehouse should reduce from his monthly storage rate to ensure that the warehouse is safe at all times. So here: Build the stand-alone ED that models Q(t). Find the equilibrium solution of DE and determine its stability type. Explain why the warehouse will eventually be in danger. Calculate the new monthly storage rate that ensured the balance was below the danger threshold. Calculate the difference between the current rate and the secure rate. Make sure you have 4 decimal places of precision in your answer!