Chapter 5.3, Problem 42E

In the treatment of prostate cancer, radioactive implants are often used. The implants are left in the patient and never removed. The amount of energy that is transmitted to the body from the implant is measured in rem units and is given by

$E={\displaystyle {\int }_0^a{P}_0{e}^{-kt}}dt,$

where k is the decay constant for the radioactive material, t is the number of years since the implant, a is the time (in years) until the rem measurement is made, and $P_0$ is the initial rate at which energy is transmitted. (Source: www.cancer.gov. Use this information for Exercises 41 and 42.

Suppose the treatment uses palladium-103, which has a half-life of 16.99 days.

a. Find the decay rate, k, of palladium-103.

b. How much energy (measured in rems) is transmitted in the first month if the initial rate of transmission is 10 rems per year?

c. What is the total amount of energy that the implant will transmit to the body?