MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This exercise uses the radioactive decay model. The half-life of cesium-137 is 30 years. Suppose we have a 14-g sample. (a) Find a function m(t) = mo2-t/ that models the mass remaining after t years. m (t ) = (b) Find a function m(t) = moet that models the mass remaining after t years. (Round your r value to four decimal places.) m(t) = (c) How much of the sample will remain after 70 years? (Round your answer to one decimal place.) g (d) After how many years will only 4 9 of the sample remain? (Round your answer to the nearest whole number.) yr 2. This exercise uses the radioactive decay model. After 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) what is the half-life of radon-222? (Round your answer to two decimal places.) days b) How long will it take the sample to decay to 30% of its original amount? (Round your answer to two decimal places.) days This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 80% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your decay rate, I, to 6 decimal places. Then round your answer to the nearest whole number.) yr This exercise uses the radioactive decay model. The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest ten years.) yr This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6F. Immediately following death, the body begins to cool. It h Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 50F. a ) Find a function T(t) that models the temperature t hours after death. T(t ) = (b) If the temperature of the body is now 790F, how long ago was the time of death? (Round your answer to the nearest whole number.) hr