By James J. Reynolds Ronald J. Harshbarger
MATHEMATICAL functions FOR THE administration, lifestyles, AND SOCIAL SCIENCES, ninth version is meant for a two-semester utilized calculus or mixed finite arithmetic and utilized calculus path. The book's concept-based process, a number of presentation tools, and engaging and correct purposes hold scholars who more often than not take the course--business, economics, existence sciences, and social sciences majors--engaged within the fabric. This version broadens the book's real-life context via including a couple of environmental technological know-how and fiscal functions. using modeling has been improved, with modeling difficulties now sincerely categorised within the examples. additionally incorporated within the 9th variation is a quick assessment of algebra to arrange scholars with assorted backgrounds for the cloth in later chapters.
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Extra resources for Mathematical Applications for the Management, Life, and Social Sciences (9th Edition)
Y3)Ϫ2 y y 31. (xy)2 32. (2m)3 33. a 2 4 b x5 34. a 8 3 b a3 In Problems 35–46, compute and simplify so that only positive exponents remain. 35. (2xϪ2y)Ϫ4 36. (Ϫ32x5)Ϫ3 Ϫ3 2 5 Ϫ4 37. (Ϫ8a b )(2a b ) 38. (Ϫ3m2yϪ1)(2mϪ3yϪ1) Ϫ2 Ϫ1 2 39. (2x ) Ϭ (x y ) 40. (Ϫ8aϪ3b2c) Ϭ (2a5b4) 3 Ϫ3 x xϪ2 Ϫ3 b 41. a Ϫ2 b 42. a y y Ϫ1 4x yϪ40 Ϫ2 aϪ2bϪ1cϪ4 Ϫ3 43. a 4 Ϫ3 0 b 44. a Ϫ2 4 Ϫ10 b ab c 2 xy (2x)Ϫ2 2xϪ2 45. (a) (b) (2x)2 (2x)2 2xϪ2 2xϪ2 (c) (d) 2 2x (2x)Ϫ2 Ϫ1 Ϫ2 2 x 2Ϫ1xϪ2 46. (a) (b) (2x)2 2x2 (2xϪ2)Ϫ1 (2xϪ2)Ϫ1 (c) (d) (2x)Ϫ2 2x2 In many applications it is often necessary to write expressions in the form cxn, where c is a constant and n is an integer.
B) For the years in (a), the actual average millions of shares traded on the NYSE were as follows. 16 What does the formula predict for these years? (c) Suppose in 2015 that a stock market average (such as the Dow Jones Industrial Average) dramatically soared or tumbled; do you think this formula’s predictions would be accurate, too low, or too high? Explain. 67. 097)Ϫt where t is the number of years past 1980. S. Fish and Wildlife Service) (a) The actual numbers of endangered species for selected years were as follows.
A) 3 1 32 3 14 (b) 116a3x 12ax Solution 3 1 32 32 3 (a) 3 ϭ 3 ϭ1 8ϭ2 B 4 14 Rationalizing (b) 116a3x 16a3x ϭ ϭ 18a2 ϭ 2a 12 B 2ax 12ax Occasionally, we wish to express a fraction containing radicals in an equivalent form that contains no radicals in the denominator. This is accomplished by multiplying the numerator and the denominator by the expression that will remove the radical. This process is called rationalizing the denominator. ● EXAMPLE 9 Rationalizing Denominators Express each of the following with no radicals in the denominator.