(Solved): Iodine-123 is a radioactive isotope used in medicine to test the function of the thyroid gland. It ...

Iodine-123 is a radioactive isotope used in medicine to test the function of the thyroid gland. Its half-life is \( 13.1 \) hours. A 400 -microcurie ( \( \mu \) Ci) dose of iodine-123 is administered to a patient. The quantity, \( Q \), left in the body after t hours is given by the equation \( Q=400\left(\frac{1}{2}\right)^{\frac{t}{13.1}} \). Answer parts (a) through (d). (a) Determine the time it takes for the level of iodine-123 to drop to \( 5 \mu \mathrm{Ci} \). It takes \( h r \) for the level of iodine-123 to drop to \( 5 \mu \mathrm{Ci} \). (Type an integer or decimal rounded to two decimal places as needed.) (b) Determine the rate of change of the quantity of iodine-123 at \( 18 \mathrm{hr} \). The rate of change of iodine-123 at \( 18 \mathrm{hr} \) is \( \mu \mathrm{Ci} / \mathrm{hr} \). (Type an integer or decimal rounded to two decimal places as needed.)