By Vladimir Ivanovich Smirnov
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Extra resources for Cours de Mathématiques Supérieures
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.
Cours de Mathématiques Supérieures by Vladimir Ivanovich Smirnov