Please solve this problem for me and show work:
When a water-cooled nuclear power plant is operating, oxygen in the water is transmuted to nitrogen 17. After the reactor is shut down, the radiation from this nitrogen 17 decreases in a such a way that teh rate of change in the radiation level is directly porportional to the radiation level.
a) Write a differential equation that expresses the rate of change of the radiation level in terms of the radiation leve. Solve the equation to find an equation that expresses the radiation level in terms of time
b) Suppose that when the reactor is first shut down, the radiaton level 3 x 10^17 units. After 60 seconds the level has dropped to 5.6 x 10^13 units. Write the particular equation.
c) It is safe to enter the reactor compartment when the radiation level has dropped to 10 x 10^-3 units. Will it be safer to enter the reactor compartment 5 minutes after the reactor has been shut down? Justify your answer.
When a water-cooled nuclear power plant is operating, oxygen in the water is transmuted to nitrogen 17. After the reactor is shut down, the radiation from this nitrogen 17 decreases in a such a way that teh rate of change in the radiation level is directly porportional to the radiation level.
a) Write a differential equation that expresses the rate of change of the radiation level in terms of the radiation leve. Solve the equation to find an equation that expresses the radiation level in terms of time
b) Suppose that when the reactor is first shut down, the radiaton level 3 x 10^17 units. After 60 seconds the level has dropped to 5.6 x 10^13 units. Write the particular equation.
c) It is safe to enter the reactor compartment when the radiation level has dropped to 10 x 10^-3 units. Will it be safer to enter the reactor compartment 5 minutes after the reactor has been shut down? Justify your answer.
