By James J. Reynolds Ronald J. Harshbarger

MATHEMATICAL purposes FOR THE administration, lifestyles, AND SOCIAL SCIENCES, ninth variation is meant for a two-semester utilized calculus or mixed finite arithmetic and utilized calculus path. The book's concept-based strategy, a number of presentation equipment, and engaging and suitable purposes retain scholars who commonly take the course--business, economics, existence sciences, and social sciences majors--engaged within the fabric. This variation broadens the book's real-life context through including a few environmental technology and monetary purposes. using modeling has been elevated, with modeling difficulties now sincerely categorised within the examples. additionally incorporated within the 9th variation is a short assessment of algebra to arrange scholars with assorted backgrounds for the fabric in later chapters.

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**Additional info for Mathematical Applications for the Management, Life, and Social Sciences (9th Edition) **

**Sample text**

What might explain this? (c) When can you be certain this equation is no longer valid? Half-life In Problems 71 and 72, use the fact that the quantity of a radioactive substance after t years is given by q ؍q0(2 ؊t͞k), where q0 is the original amount of radioactive material and k is its half-life (the number of years it takes for half the radioactive substance to decay). 71. The half-life of strontium-90 is 25 years. Find the amount of strontium-90 remaining after 10 years if q0 ϭ 98 kg. 72.

Perform additions and subtractions from left to right. ● EXAMPLE 3 Order of Operations Evaluate the following. (a) Ϫ4 ϩ 3 (b) Ϫ42 ϩ 3 (c) (Ϫ4 ϩ 3)2 ϩ 3 (d) 6 Ϭ 2(2 ϩ 1) Solution (a) Ϫ1 (b) Note that with Ϫ42 the power 2 is applied only to 4, not to Ϫ4 (which would be written (Ϫ4)2). 2 The Real Numbers ● ● Checkpoint True or false: 4. Ϫ(Ϫ5)2 ϭ 25 5. 0 4 Ϫ 6 0 ϭ 0 4 0 Ϫ 0 6 0 6. 9 Ϫ 2(2)(Ϫ10) ϭ 7(2)(Ϫ10) ϭ Ϫ140 The text assumes that you have a scientiﬁc or graphing calculator. Discussions of some of the capabilities of graphing calculators and graphing utilities will be found throughout the text.

Checkpoint Solutions 1. (a) Meaningless. A denominator of zero means division by zero, which is undeﬁned. (b) 04 ϭ 0. A numerator of zero (when the denominator is not zero) means the fraction has value 0. 4 (c) ϭ 1 4 (d) Meaningless. The denominator is zero. 2. (a) 1 Ͻ x Ͻ 3 (b) 0 Ͻ x Յ 3 (c) Ϫ1 Յ x Ͻ q or x Ն Ϫ1 (d) Ϫq Ͻ x Ͻ 2 or x Ͻ 2 0 1 2 3 0 1 2 3 –2 –1 0 1 3. (a) 33, 64; closed interval (b) 3Ϫ6, 4); half-open interval 4. False. Ϫ(Ϫ5)2 ϭ (Ϫ1)(Ϫ5)2 ϭ (Ϫ1)(25) ϭ Ϫ25. Exponentiation has priority and applies only to Ϫ5.