When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17. After the reactor is
shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level. Required:
Write a differential equation that expresses the rate of change in the radiation level in terms of the radiation level.
Differential equation for the rate of change in radiation level:
Radiation level is R.
Rate of change indicates that the radiation level R varies in function of time t, which mathematically means that we have:
After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportional to the radiation level.
Rate of change is k. Decreases means that k is negative. Proportional to the radiation level of R means that -k multiplies R. So the differential equation is:
when a line is parallel to another line that means the slip of the lines are going to be the same and since the y-intercept of the other line was given to you, you would just put them together in one equation.
