Concept explainers
Setting Up Equations Each of Exercise S-1 through S-4 poses a question that can be answered by solving an equation. Given the appropriate equation. Note that you are not asked to solve the equation.
Argon-39 is a radioactive isotope of argon. Initially a sample of argon-39 contains 10 grams, and the amount remaining after t years is given by
The half-life is the time required for the amount of argon-39 to be reduced by half. The half-life of argon-39 is the solution of an equation. Find that equation.
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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?arrow_forwardThe Crossing-Graphs Method In Exercise S-5 through S-16, use the crossing-graphs method to solve the given equation. x2-x3+3=x520arrow_forwardDrug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forward
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