Chapter 9 Radical Functions

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Homework 9.6 SSM: Intermediate Algebra 11. ( 2,6 ) and ( 5,4 ) Substitute the points into the equation y a x b = + . 6 = a 2 + b 4 = a 5 + b Rewrite as: 1.4142a + b = 6 2.2361a + b = 4 Solve the resulting system. Multiply the first equation by − 1 and add to the second equation. −1.4142a − b = −6 2.2361a + b = 4 0.8129a = −2 a ≈ −2.43 2,6 into the equation Substitute the point ( ) y = − 2.43 x + b and solve for b. 6 = − 2.43 2 + b b ≈ 9.44 The equation is roughly y = − 2.43 x + 9.44 . 13. Increase the value of b to shift the graph up. 15. a. Start by plotting the data. ( ) = 5.65 t + 10 f t b. f ( 26) = 5.65 ( 26) + 10 ≈ 38.81 c. In 2008, 38.8% of single-parent fathers will have never been married. 5.65 t + 10 = 39 5.65 t = 29 ( t ) t = 29 5.65 2 ⎛ 29 ⎞ = ⎜ 5.65 ⎟ ⎝ ⎠ t ≈ 26.35 In 2008, 39% of single-parent fathers will have never been married. d. ( 0,10 ) . In 1982, 10% of single-parent fathers had never been married. 17. a. Start by plotting the data. 2 Answers may vary. A square root model 0,10 may be reasonable. Use the points ( ) and ( 18,34 ) . Substitute the point ( 0,10 ) into the equation y = a x + b . 10 = a 0 + b b = 10 Substitute the point ( ) 18,34 into the equation y = a x + 10 and solve for a. 34 = a 18 + 10 24 a = ≈ 5.66 18 Answers may vary. A square root model seems to be appropriate. Use the points 52.5,1.94 . ( 0,0 ) and ( ) Substitute the point ( 0,0 ) into the equation y = a x + b . 0 = a 0 + b b = 0 52.5,1.94 into the Substitute the point ( ) equation y = a x and solve for a. 1.94 = a 52.5 a ≈ 0.27 S h = ( ) 0.27 h 298
SSM: Intermediate Algebra Homework 9.6 b. i. Graph all three functions. 19. a. Start by plotting the data. The model S ( h ) appears to fit the best. ii. S ( ) L( ) Q( ) iii. 0 = 0; 0 = 0.327; 0 = 0.165 S models the situation best near 0 since it is the only model that passes through the origin. Zoom out. Q is not possible since it indicates that the falling time will reach 0 for larger drop heights. Answers may vary. A square root model seems reasonable. 3,68 . Use the points ( 0,0 ) and ( ) Substitute the point ( 0,0 ) in the equation y = a x + b . 0 = a 0 + b b = 0 Substitute the point ( ) y = a x and solve for a. 68 = a 3 a ≈ 39.26 S t = ( ) 39.26 t 3,68 into the equation iv. v. S models the situation the best and has no problems with larger h. T = = 2h 32.2 2 32.2 = 0.249 h This is close to the model ( ) 0.27 S h h = h . b. i. Both models seem to fit the data pretty well but the square root model seems to be a little better fit. c. 0.27 h = 3 ( h ) h = 3 0.27 2 2 ⎛ 3 ⎞ = ⎜ ⎟ ⎝ 0.27 ⎠ h ≈ 123.46 According to the model, the height of the cliff is roughly 123.46 feet. d. S ( 1250) = 0.27 1250 ≈ 9.55 It would take about 9.55 seconds for the baseball to reach the ground if it were dropped from the top of New York City’s Empire State Building. ii. As the length of release time increases, the percent of criminals that were arrested again cannot decrease since the percentages are cumulative. The square root function is an increasing function. c. ( ) 4 39.26 4 78.52 S = = About 78.5% of convicts released from state prison have been arrested for another crime after being out of prison for 4 years or less. 299
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Chapter 9 Radical Functions

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