508 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 16. Decay of Plutonium Repeat Exercise 15 for 500 g of plutonium-241, which decays according to the function A1t2 = A0 e-0.053t, where t is time in years. 17. Decay of Radium Find the half-life, to the nearest hundred years, of radium-226, which decays according to the function A1t2 = A0 e-0.00043t, where t is time in years. 18. Decay of Tritium Find the half-life, to the nearest year, of tritium, a radioactive isotope of hydrogen, which decays according to the function A1t2 = A0 e-0.056t, where t is time in years. 19. Radioactive Decay If 12 g of a radioactive substance are present initially and 4 yr later only 6.0 g remain, how much of the substance, to the nearest tenth of a gram, will be present after 7 yr? 20. Radioactive Decay If 1 g of strontium-90 is present initially, and 2 yr later 0.95 g remains, how much strontium-90, to the nearest hundredth of a gram, will be present after 5 yr? 21. Decay of Iodine How long, to the nearest day, will it take any quantity of iodine-131 to decay to 25% of its initial amount, knowing that it decays according to the exponential function A1t2 = A0 e-0.087t, where t is time in days? 22. Magnitude of a Star The magnitude M of a star is modeled by M= 6 - 5 2 log I I0 , where I0 is the intensity of a just-visible star and I is the actual intensity of the star being measured. The dimmest stars are of magnitude 6, and the brightest are of magnitude 1. Determine the ratio of light intensities between a star of magnitude 1 and a star of magnitude 3. 23. Carbon-14 Dating Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about one-third the amount found in living human beings. How long ago, to the nearest hundred years, did the Egyptian die? 24. Carbon-14 Dating A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 of a contemporary sample. How old was the sample? Round to the nearest hundred years. 25. Carbon-14 Dating Paint from the Lascaux caves of France contains 15% of the normal amount of carbon-14. Estimate the age of the paintings. Round to the nearest hundred years. 26. Dissolving a Chemical The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model A1t2 = 10e0.0095t. At what temperature, to the nearest degree (Celsius), will 15 g dissolve? 27. Newton’s Law of Cooling Boiling water, at 100°C, is placed in a freezer at 0°C. The temperature of the water is 50°C after 24 min. Find the temperature of the water to the nearest hundredth after 96 min. (Hint: Change minutes to hours.) 28. Newton’s Law of Cooling A piece of metal is heated to 300°C and then placed in a cooling liquid at 50°C. After 4 min, the metal has cooled to 175°C. Find its temperature to the nearest hundredth after 12 min. (Hint: Change minutes to hours.) Finance (Exercises 29–34) 29. Comparing Investments Russ, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 3% compounded quarterly. Another offers 2.75% compounded continuously. (a) Which investment will earn more interest in 5 yr? (b) How much more will the better plan earn?
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