Carbon Dating The age of an ancient artifact can be deter-mined by the amount of radioactive carbon-14 remaining in it.If Do is the original amount of carbon-14 and D is the amountremaining, then the artifact's age A (in years) is given byA = -8267 InDoFind the age of an object if the amount D of carbon-14 thatremains in the object is 73% of the original amount Dg-

Answered: Carbon Dating The age of an ancient…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.3: Logarithmic Functions

Problem 97E

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An Uncertain Investment Suppose you invested 1300 in the stock market two years ago. During the first year the value of the stock increased by 12%. During the second year, the value of the stock decreased by 12%. How much money is your investment worth at the end of the two-year period? Did you earn money or lose money? Note: The answer to the first question is not 1300
Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20000(0.90) and the value of the car after the end of the second year would be $20000(0.90)2. Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.
Forensics At 8:30 A.M., a coroner went to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person’s temperature twice. At 9:00 A.M. the temperature was 85.7F, and at 11:00 A.M. the temperature was 82.8F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula t=10lnT7098.670 where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person’s body. (This formula comes from a general cooling principle called Newton’s Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6F at death and that the room temperature was a constant 70F.) Use the formula to estimate the time of death of the person.
Radioactive Decay The half-life of a radioactive substance is the time H that it takes for half of the substance to change form through radioactive decay. This number does not depend on the amount with which you start. For example, carbon-14 is known to have a half-life of H=5770 years. Thus, if you begin with 1 gram of carbon-14, then 5770 years later you will have 12 gram of carbon-14. And if you begin with 30 grams of carbon-14, then after 5770 years there will be 15 grams left. In general, radioactive substances decay according to the formula A=A00.5tH Where H is the half-life, t is the elapsed time, A0 is the amount you start with the amount when t=0, and A is the amount left at time t. a. Uranium-228 has a half-life H of 9.3 minutes. Thus, the decay function for this isotope of uranium is A=A00.5t9.3, where t is measured in minutes. Suppose we start with grams of uranium-228. i. How much uranium-228 is left after 2 minutes? ii.How long will you have to wait until there are only 3 grams left? b. Uranium-235 is the isotope of uranium that can be used to make nuclear bombs. It has a half-life of 713 million years. Suppose we start with 5 grams of uranium-235. i. How much uranium-235 is left after 200 million years? ii. How long will you have to wait until there are only 3 grams left?
pH of Saliva The pH of saliva is normally in the range of 6.4 to 7.0. However, when a person is ill, the persons saliva becomes more acidic. a When Marco is sick, he tests the pH of his saliva and finds that it is 5.5. What is the hydrogen ion concentration of his saliva? b Will the hydrogen ion concentration in Marcos saliva increase or decrease as he gets better? c After Marco recovers, he tests the pH of his saliva, and it is 6.5. Was the saliva more acidic or less acidic when he was sick?

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