By Vladimir Ivanovich Smirnov

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49) ϭ 490 grams. 29. If a substance that is decaying exponentially decays to 40 percent of its original value in 5 years, will it decay to 40 percent of its 5-year value in the next 5 years? Yes. Let y ϭ y0at be the formula for the amount of the quantity in t years. 4 ϭ a5. 4y0) ϭ a5(a5y0) ϭ y0a10. Hence, in 10 years, y is 40 percent of its 5-year value, which is 16 percent of its original value. 30. 27? 1 days. 8) CHAP. 31. 5 percent per year, what is its half-life? 995. 3 years. 32. The half-life of a radioactive substance is 125 years.

20. The population of a small country is growing exponentially and doubled in 10 years. will the population triple? Let P denote the population, and let time t be measured in years. 0718. 0718) . 8 years. 21. 045. time for the population? 75 time units. 22. 5 percent per year. the population? 075. 6 years. 23. A population is growing exponentially at 8 percent every 10 years. The doubling time What is the doubling time? 08(2) ϭ ᎏᎏ ≈ 9. 08) population doubles in 90 years. 24. [CHAP. 8 percent every year?

1-18(b)]. This is the common graph. (a) 3x ϩ 2y ϭ 0 Fig. 1-18 (b) y ϭ 3x ϩ 5 CHAP. 13. Find the slope m of the line L through (a) P(1, 3), Q(5, 6); (b) P(1, 1), Q(2, 11); (c) P(1, 6), Q(5, 3); (d ) P(2, 11), Q(3, 1). Without drawing the lines, determine which lines are rising, which lines are falling, and which are steeper. y2 Ϫ y1 To find the slope m, use the formula m ϭ ᎏ : x2 Ϫ x1 6Ϫ3 5Ϫ1 3 4 (a) m ϭ ᎏ ϭ ᎏ 11 Ϫ 1 2Ϫ1 (b) m ϭ ᎏ ϭ 10 3Ϫ6 5Ϫ1 3 4 (c) m ϭ ᎏ ϭ Ϫ ᎏ 1 Ϫ 11 3Ϫ2 (d ) m ϭ ᎏ ϭ Ϫ 10 Lines (a) and (b) are rising, since their slopes are positive, and (b) is steeper than (a), since the magnitude of its slope is larger.

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Cours de Mathématiques Supérieures by Vladimir Ivanovich Smirnov


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