Roughly 12,000 Americans are diagnosed with thyroid cancer every year, which accounts for 1% of all cancer cases. It occurs in women three times as frequently as in men. Fortunately, thyroid cancer can be treated successfully in many cases with radioactive iodine, or I-131. This unstable form of iodine has a half-life of 8 days and is given in small doses measured in millicuries.

a. Suppose a patient is given an initial dose of 100 millicuries. Find the function that gives the amount of I-131 in the body after t ≥ 0 days.

b. How long does it take the amount of I-131 to reach 10% of the initial dose?

c. Finding the initial dose to give a particular patient is a critical calculation. How does the time to reach 10% of the initial dose change if the initial dose is increased by 5%?