,3 . . L33 . . . . The Isotope of plutonium P11 is used to make thermoelectric power sources for spacecraft. Suppose that a space probe Iwas launched in 2012 with 2.5 kg of 238 Pu. Part: I] l 2 Part 1 of2 (a) If the halflife of 233P11 is 817 yr, write a function of the form Q (I) = QOE h to model the quantity Q (I) of 238Pu left after I years. Round the value of k to ve decimal places. Do not round intermediate calculations. _ U IE' Technetium99 (meC) is a radionuclide used widely in nuclear medicine. mec is combined with another substance that is readin absorbed by a targeted body organ. Then, special cameras sensitive to the gamma rays emitted by the technetium are used to record pictures of the organ. Suppose that a technician 99 . . . . prepares a sample of mTc-pyrophosphate to Image the heart of a patient suspected of haying had a mild heart attack. Part: Of 2 Part 1 of2 (a) At noon, the patient is given 10 mCi (millicun'es) of meC. If the halflife of mec is 6 1:1, write a function of the form Q (I) = QUEM to model the radioactivity level Q {I} after I hours. Round k to four decimal places. Do not round intermediate calculations. The radioactiyity level function is Q (r) = _ . LID r X 53 Fluorodeoxvglucose is a derivative of glucose that contains the radionuclide uorine-18 (13F) A patient is given a sample of this material containing 300 hIBq of 18 F (a megabecquerel is a unit of radioactivity). The patient then undergoes a PET scan (positron emission tomography) to detect areas of metabolic activity indicative of cancer. After 17"4 min, onethird of the original dose remains in the body. Part: I] l 2 Part 1 of2 (a) Write a function of the form Q {t} = Queh to model the radioactivity level Q {I} of fluorine-18 at a time t minutes after the intial dose. Round the value of k to ve decimal places. Do not round intermediate calculations. em = [I Um .. X 53