Technetium-99m (abbreviated 99m Tc) is a short-lived gamma-ray emitter that is used in nuclear medicine. Suppose that a patient is given a small amount of 99m Tc for a diagnostic test. Further suppose that the amount of 99m Tc decays exponentially according to the model Q(t) = Q0e−kt. The value Q0 is the initial amount administered, and Q(t) represents the amount of 99m Tc remaining after t hours. The value of k is the decay constant. a. If 94% of the technetium has decayed after 24 hr (that is, 6% remains), determine the value of k. Round to 3 decimal places. b. If 30 mCi is initially given to a patient for blood pool imaging of the heart, determine the amount remaining after 10 hr. Round to 1 decimal place. c. Determine the amount of time required for the amount of 99m Tc to fall below 1% of the original amount given. Round to 1 decimal place.
Technetium-99m (abbreviated 99m Tc) is a short-lived gamma-ray emitter that is used in nuclear medicine. Suppose that a patient is given a small amount of 99m Tc for a diagnostic test. Further suppose that the amount of 99m Tc decays exponentially according to the model Q(t) = Q0e−kt. The value Q0 is the initial amount administered, and Q(t) represents the amount of 99m Tc remaining after t hours. The value of k is the decay constant.
a. If 94% of the technetium has decayed after 24 hr (that is, 6% remains), determine the value of k. Round to 3 decimal places.
b. If 30 mCi is initially given to a patient for blood pool imaging of the heart, determine the amount remaining after 10 hr. Round to 1 decimal place.
c. Determine the amount of time required for the amount of 99m Tc to fall below 1% of the original amount given. Round to 1 decimal place.
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