I1 the population to A.Evaluatey= 2e ) 2. When will the population reach 3 million? B. Solve 2e.02 6. 3. How large will the population be in 3 yr? C.Evaluate y= 2e023) 4. How large will the population be in 4 months? D.Solve 2e.02 3 CONCEPT PREVIEW Radioactive Decay Strontium-90 decays according to the expo- nential function yyoe 0.0241 where t is time in years. Match each question in Column I with the correct procedure in Column Il to answer the question. I II 5. If the initial amount of Strontium-90 is 200 g, A.Solve 0.75yo yoe 0.0241t how much will remain after 10 yr? 6. If the initial amount of Strontium-90 is 200 g, how much will remain after 20 yr? B.Evaluate y = 200e .0241 (10) 7. What is the half-life of Strontium-90? C. Solve yo yoe 0.0241r. 8. How long will it take for any amount of Strontium-90 to decay to 75% of its initial D.Evaluate y = 200e 0.0241 (20) amount? (Modeling) exponential or logarithmic models. See Examples 1-6. The exercises in this set are grouped according to discipline. They involve Physical Sciences (Exercises 9-28) An initial amount of a radioactive substance yo is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = yo ekt that mode ls the situation, give the exact value of k in terms of natural logarithms. After 6 hr, 10 g remain. 10. Уo - 30 gs 9. yo= 60 g; After 3 hr, 20 g remain. 12. yo = 20 mg; The half-life is 200 days. 11. yo = 10 mg; The half-life is 100 days. 14. yo= 8.1 kg; After 4 yr, O.9 kg remains. 2.4 lb; After 2 yr, 0.6 lb remains. 13. yo 15. Decay of Lead A sample of 500 g of radioactive lead-210 decays to polonium-210 according to the function Solve each problem. A(t) = 500e 0.032; where t is time in years. Find the amount of radioactive lead remaining after (c) 20 yr. (d) Find the half-life. (b) 8 yr, (а) 4 yr, ల
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
15.
How do you answer part (a) and (d)?
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