Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 1 - Test - Page 101: 8

Answer

The model underestimates the percentage of Americans by $1.9\%$.

Work Step by Step

The mathematical model: $$P = -0.5x^{2} + 0.1x + 26.9$$ describes the percentage of Americans, $P$, in age group $x$ who had contact with a police officer. Based on the graph, age group 20-29 is classified as Group 2; therefore, in this case, $x=2$. Substituting this to the equation: $$P = -0.5x^{2} + 0.1x + 26.9$$ $$P = -0.5(2)^{2} + 0.1(2) + 26.9$$ $$P = -0.5(4) + 0.2 + 26.9$$ $$P = -2 + 0.2 + 26.9$$ $$P = 25.1\%$$ The graph shows that $27\%$ of Americans in age group 20-29 had contact with a police officer. Therefore, the model underestimates the percentage of Americans by: $$27-25.1=1.9\%$$
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