Explanation Given: The polynomial y = 0.0790 x 3 − 2.103 x 2 + 10.695 x + 179.504 represents the number of births to females, in thousands, in the United States under 15 and 17 years of age with x represents the number of years after 1990. The model indicates that 155,154 births occurred in 2000. Procedure used: Synthetic division method: “To divide a polynomial by ( x − a ) : 1. Arrange the coefficients in descending powers of x , with a 0 for any missing power. Place a from ( x − a ) to the left of the coefficients. 2. Bring down the first coefficient to the third line. Multiply the last number in the third line by a and write the product in the second line under the next term. 3. Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. 4. The third line represents the coefficients of the quotient, with the last number the remainder. The quotient is a polynomial of degree one less than the dividend. If the remainder is 0, x − a is a factor of the polynomial, and the polynomial can be written as the product of the divisor x − a and the quotient.” Calculation: The polynomial function is y = 0.0790 x 3 − 2.103 x 2 + 10.695 x + 179.504 . Since x represents the number of years after 1990, the value of x is 10 for year 2000. The females birth occurs 155,154 for x = 10 . Since y is the number of births in thousands, the value of y ( 10 ) = 155.154 . Thus, x = 10 satisfies the equation y ( 10 ) = 155.154 . That is, the term x − 10 is factor of the polynomial 0.0790 x 3 − 2.103 x 2 + 10.695 x + 179.504 = 155.154 . 0.0790 x 3 − 2.103 x 2 + 10.695 x + 179.504 − 155.154 = 0 0.0790 x 3 − 2.103 x 2 + 10.695 x + 24.35 = 0 Divide the polynomial 0.0790 x 3 − 2.103 x 2 + 10.695 x + 24.35 = 0 by x − 10 . Set the coefficients in descending powers of x , 0 .0790 − 2.103 10 .695 24 .35 Set 24 from x − 24 to the left of the coefficients. 10 0 .0790 − 2.103 10 .695 24 .35 Use step 2 and 3 mentioned in Synthetic division method that is bring 0.0790 to the last entry (that is, last from the right end) of third line and multiply 0.0790 by a , which is 10 and write the product 0.790 in second line under next term and add the number 0.790 in the second line and the number above –2.103 in first line. Continue this process and obtain the result as follows, 10 0 .0790 − 2.103 10 .695 24 .35 0

5th Edition

ISBN: 9780134179926

Author: HARSHBARGER

Publisher: PEARSON CO

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Chapter 6.4, Problem 41E

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To find: The years other than 2000 when the model noticed that 155,154 births occurred.

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Chapter 6.4, Problem 40E

Chapter 6.4, Problem 42E

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Chapter 6 Solutions

EBK COLLEGE ALG.IN CONTEXT W/APPL.F/MAN

Ch. 6.1 - Graph the function h(x) = 3x3 + 5x2 x 10 on the...Ch. 6.1 - Graph the function f(x) = 2x3 3x2 6x on the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - For Exercises 1116, match the polynomial function...Ch. 6.1 - For Exercises 1720, use the equation of the...Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Sketch a graph of any cubic polynomial function...Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Daily Revenue The daily revenue in dollars from...Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Starbucks Using data from 2005 and projected to...Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Salaries The median salary for male workers, in...Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.2 - Find the cubic function that models the data in...Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Prob. 3E Ch. 6.2 - Find the quartic function that is the best fit for...Ch. 6.2 - Prob. 5E Ch. 6.2 - a. 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The years other than 2000 when the model noticed that 155,154 births occurred.

Solution Summary: The author explains how the polynomial y represents the number of births to females in the United States under 15 and 17 years of age.

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Chapter 6 Solutions