\fThe populations of two countries are given for January 1, 2000, and for January 1, 2010. Part: 0 / 3 Part 1 of 3 (a) Write a function of the form P (t) = Poe" to model each population P () (in millions) & years after January 1, 2000. Round the value of * to five decimal places. Country Population Population in 2000 P (t) = Pe in 2010 e (millions) (millions) X 50 66 P (t) = 5 Congo Turkey 67.4 73.7 P (t) =.., The isotope of plutonium ASBPU is used to make thermoelectric power sources for spacecraft. Suppose that a space probe was launched in 2012 with 2.5 kg of 238 Pu. Part 1 of2 (a) If the halflife of 235I'Pu is 87.? 3'1, write a function of the form Q (r) = Queh to model the quantity Q (I) of 238P11 left after it years. Round the value of k to ve decimal places. Do not round intermediate calculations. .E-3 Q (f) = i 258 000.90: Alternate Answer: 233 (b) If 1.4 kg of P11 is required to power the spacecraft's data transmitter, for how long after launch would scientists be able to receive data? Round to the nearest year. Do not round intermediate calculations. X 8 Scientists will be able to receive data for approximately I I 3-\"1'. ' Fluorodeoxvglucose is a derivative of glucose that contains the radionuclide Fluorine13 (18F). A patient is given a sample of this material containing 300 MIBq of 18 . . . . . . . . . . . . F (a megabecquerel Is a unit of radioactIVIty). The patient then undergoes a PEI' scan (pDSItron 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 10f2 o (a) Write a function of the form QC) =Qt2kf to model the radioactivity level Q'EI} of fluorine-13 at a time t minutes after the intial dose. Round the value of k to ve decimal places. Do not round intermediate calculations. Q (1') = 30020305311' Part:1/2 Part 2 of2 (b) what is the halflife of 18F? Round to the nearest minute. Do not round intermediate calculations. 13 _ . The halflife of F is approximately l_l mm. X 5 Technetium99 (mec) is a radionuclide used widely in nuclear medicine. meC is combined with another substance that is readily 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 prepares a sample of 99mTc-pyrophosphate to image the heart of a patient suspected of having had a mild heart attack. Part 10f2 a (a) At noon, the patient is given 10 mCi (millicun'es) of 9ngc. If the half-life of 99mTc is 6 hr, write a function of the form Q (I) = Queh to model the radioactivity level er} after? hours. Round kto four decimal places. Do not round intermediate calculations. U.1153I The radioactivity level function is Q (I) =' 102 '. Part:1/2 Part 2 of2 (b) At what time will the level of radioactivity reach 4 mCi? Round to the nearest tenth of an hour. The level of radioactivity will reach 4 IIICi after approximately |_| hi. X 53