AN42 Answers: Chapter 5 23. (a) P 0 3.2; ( ) = In 2010, about 3.2% of U.S. households owned a tablet computer. (b) 0 60 10 0 (c) 50.7% (d) During 2015 25. (a) 120 0 0 100 (b) 0.78, or 78% (c) 50 people (d) As n increases, the probability decreases. 27. (a) P 0 48; ( ) ≈ In 1900, about 48 invasive species were present in the Great Lakes. (b) 1.7% (c) 225 0 0 120 (d) About 176 (e) During 1999 5. (a) 0 250 0 350 (b) y x 371.7593 42.2140 ln = − (c) 0 250 0 350 (d) 194 billion pounds (e) Over by 4 billion pounds 7. (a) 350 210 0 130 (b) y e 655.5459 1 7.4740 x 0.0171 = + − (c) 210 0 350 130 (d) 655.5 million (e) 348.4 million ≈ (f) about 2035 9. (a) 22 12 65 95 (b) Linear (c) y x 0.2119 0.3091 = − (d) 22 12 65 95 (e) 16.6 chirps per second 11. (a) 0 110 0 30 (b) Exponential (c) y 115.5779 0.9012 x ( ) = (d) 0 0 110 30 (e) 5.1% 12. f x x x x 1 3 3 1 2 2 ( ) ( )( ) ( ) = + + − 13. 3 14. y 10 −10 x 10 −10 15. 3, 2 ( ) − − 16. f x x 4 ( ) = − − 17. 2 19 3 , 2 19 3 { } − + 18. { } − < ≤ − > x x x 5 1 or 5 or 5, 1 5, ( ] ( ) − − ∪ ∞ 19. R f 3 0; ( ) = − = yes 20. 6 21. The function f is a polynomial so it is a continuous function, and f f 2 21; 1 3; ( ) ( ) − = − − = zero: 1.32 − Review Exercises (page 376) 1. (a) 26 − (b) 241 − (c) 16 (d) 1− 2. (a) 11 (b) 1 (c) 6 2 + (d) 19 3. (a) e4 (b) e3 2 2 − − (c) ee4 (d) 17 − 4. f g x x 1 3 , ( )( ) = − all real numbers; g f x x 7 3 , ( )( ) = − all real numbers; f f x x, ( )( ) = all real numbers; g g x x9 4, ( )( ) = + all real numbers 5. f g x x x 3 3 3 , 2 ( )( ) = + + all real numbers; g f x x x x x f f x x x x 1 3 3 , 0 ; 3 3 , 0 ( ) ( ) ( ) { } ( ) { } = + + ≥ = ≥ ; g g x x x x x 3 3 4 2 , 2 3 4 ( )( ) = + + + + all real numbers 29. (a) P t 50 3t 20 ( ) = ⋅ (b) 0 0 750 50 (c) 661 (d) In 48 days (e) P t e 50 t 0.055 ( ) = 31. ( ) = − + f x x 3 2 7 32. Neither 33. x y z 2 ln 1 2 ln ln + − 34. x x x 4, 2 { } ≠ − ≠ 35. g f x x x x x 2 13 3 4 2 ( )( ) ( )( ) − = − − − − 36. x-intercepts: 5 17 4 , 5 17 4 ; − + y-intercept: 1 37. { } − 2 2 , 2 2 38. y x r 1.0714 3.9048; 0.985 = − + = − 39. 23 3 210 10 Local minima: f 1.37 5.85 ( ) − = − and f 1 1 ( ) = − Local maximum: f 0.37 0.65 ( ) = − Increasing: 1.37, 0.37 1, 3 [ ] [ ] − ∪ Decreasing: 3, 1.37 0.37, 1 [ ] [ ] − − ∪ 40. x x 40 45 3 2 3 2 3 ( ) + + 1. (a) 200,000 0 45 0 (b) y 11.1287 1.2794 x ( ) = (c) N t e 11.1287 t 0.2464 ( ) = (d) 200,000 0 45 0 (e) 727,328 (f ) April 6 3. (a) 100 0 20 4 (b) y 118.7226 0.7013 x ( ) = (c) A t e 118.7226 t 0.3548 ( ) = − (d) 100 0 20 4 (e) 28.7% (f ) k 0.3548 35.48% =− =− is the exponential growth rate. It represents the rate at which the percentage of patients surviving advanced-stage breast cancer is decreasing. 5.9 Assess Your Understanding (page 370)
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