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lana66690 [7]
3 years ago
8

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.
Mathematics
1 answer:
wolverine [178]3 years ago
7 0

Answer:

The differential equation is \frac{dR}{dt} = -kR

Step-by-step explanation:

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:

\frac{dR}{dt}

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:

\frac{dR}{dt} = -kR

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