W0i1380995&questionld-32;&flushe; MAT-144-TR700B Tr omework: Homework Week 9 cor
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W0i1380995&questionld-32;&flushe; MAT-144-TR700B Tr omework: Homework Week 9 core: 0 of 2 pts 41 of41 (41 complete) 5.4.28 The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 54.4% in 1990 to 50.1% in 2000. a. Predict when the percentage will be 46%. b. Predict the percentage in 2005. a. The percentage will be 46% around the year (Simplify your answer. Round to the nearest year as needed.) Enter your answer in the answer box and then click Check Answer Clear All part remaining Type here to searchExplanation / Answer
Let the linear relationship representing the number(y) of automobile consumers under 50 years of age , be y = a-bx where x is the number of years from 1990, and a is the percentage of automobile consumers under 50 years of age, in 1990. Then a = 54.4. Further, when x = 10, we have y = 50.1 so that 50.1 = 54.4-10b or, 10b = 54.4-50.1 = 4.3 so that b = 4.3/10 = 0.43. Then, the linear relationship representing the number(y) of automobile consumers under 50 years of age, is y = 54.4 -0.43x.
a. when y = 46, we have 46 = 54.4-0.43x or, 0.43x = 54.4-46 = 8.4 so that x = 8.4/0.43 =19.53. Hence, the percentage will be 46 % around the year 1990+20 = 2010( on rounding to nearest year).
b. In 2005, x = 2005-1990 =15 so that the percentage in 2005 will be 54.4-0.43*15 = 54.4-6.45 = 47.95, say, 48 %.
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