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Section 3.6 Nonlinear Models 255 35. ––CONTINUED–– (b) 300 4 14 0 Linear model: Logarithmic model: Quadratic model: 300 300 300 4 14 0 Exponential model: 4 14 0 Power model: 4 14 0 300 300 4 14 0 4 14 0 (c) Linear: 803.9 Logarithmic: 411.7 Quadratic: 289.8 (Best) Exponential: 1611.4 Power: 667.1 (d) Linear: 0.9485 Logarithmic: 0.9736 Quadratic: 0.9814 (Best) Exponential: 0.9274 Power: 0.9720 (e) Quadratic model is best. 36. Answers will vary. 37. True 38. False. Write b as b e ln b . Then, y ab x ae ln bx ae cx . © Houghton Mifflin Company. All rights reserved. 39. 2x 5y 10 40. Slope: y-intercept: 0, 2 5 4 3 1 5y 2x 10 y y 2 5 x 2 2 5 −2 −1 −1 1 2 3 4 5 −2 −3 x 3x 2y 9 Slope: y-intercept: 2 1 y y 3 2 x 9 2 3 2 0, 9 2 −2 −1 −1 1 2 3 4 5 6 −2 −3 −4 x
256 Chapter 3 Exponential and Logarithmic Functions 41. 1.2x 3.5y 10.5 42. 10 8 6 2 y −4 −2 −2 2 4 6 8 −4 −6 35y 12x 105 Slope: y-intercept: 0, 3 12 35 y 12 35 x 105 35 12 35 x 3 x 0.4x 2.5y 12.0 4 Slope: 25 0.16 y-intercept: 0, 24 5 0, 4.8 2 1 y −2 −1 −1 1 2 3 4 5 6 −2 −3 −4 −6 25y 4x 120 y 4 25 x 24 5 x Review Exercises for Chapter 3 1. 1.45 2 10.32542. 7 11 0.002 3. 60 21.1 60 2.2 0.0001225 0.0 4. 25 332 5.12 10 7 0 5. e 8 2980.958 6. 5e 5 46.7823 7. e 2.1 e 2.1 8.1662 8. 4e 35 2.1952 9. fx 4 x 10. Intercept: 0, 1 Horizontal asymptote: x-axis Increasing on: , Matches graph (c). 11. fx 4 x 12. Intercept: 0, 1 Horizontal asymptote: x-axis Decreasing on: , Matches graph (b). fx 4 x Intercept: 0,1 Horizontal asymptote: x-axis Decreasing on: , Matches graph (d). fx 4 x 1 Intercept: 0, 2 Horizontal asymptote: y 1 Increasing on: , Matches graph (a). © Houghton Mifflin Company. All rights reserved.
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256 Chapter 3 Exponential and Logarithmic Functions<br />
41.<br />
1.2x 3.5y 10.5 42.<br />
10<br />
8<br />
6<br />
2<br />
y<br />
−4 −2<br />
−2<br />
2 4 6 8<br />
−4<br />
−6<br />
35y 12x 105<br />
Slope:<br />
y-intercept:<br />
0, 3<br />
12<br />
35<br />
y 12<br />
35 x 105<br />
35<br />
12<br />
35 x 3<br />
x<br />
0.4x 2.5y 12.0<br />
4<br />
Slope: 25 0.16<br />
y-intercept: 0, 24 5 0, 4.8<br />
2<br />
1<br />
y<br />
−2 −1<br />
−1<br />
1 2 3 4 5 6<br />
−2<br />
−3<br />
−4<br />
−6<br />
25y 4x 120<br />
y 4 25 x 24<br />
5<br />
x<br />
Review Exercises for Chapter 3<br />
1. 1.45 2 10.32542. 7 11 0.002 3.<br />
60 21.1 60 2.2<br />
0.0001225 0.0<br />
4. 25 332 5.12 10 7 0 5. e 8 2980.958 6. 5e 5 46.7823<br />
7. e 2.1 e 2.1 8.1662 8. 4e 35 2.1952<br />
9. fx 4 x 10.<br />
Intercept: 0, 1<br />
Horizontal asymptote:<br />
x-axis<br />
Increasing on: , <br />
Matches graph (c).<br />
11. fx 4 x 12.<br />
Intercept: 0, 1<br />
Horizontal asymptote:<br />
x-axis<br />
Decreasing on: , <br />
Matches graph (b).<br />
fx 4 x<br />
Intercept: 0,1<br />
Horizontal asymptote:<br />
x-axis<br />
Decreasing on: , <br />
Matches graph (d).<br />
fx 4 x 1<br />
Intercept: 0, 2<br />
Horizontal asymptote: y 1<br />
Increasing on: , <br />
Matches graph (a).<br />
© Houghton Mifflin Company. All rights reserved.
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