Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.1 Algebraic Expressions and Formulas - Exercise Set 6.1 - Page 348: 69

Answer

The number of calories needed between the age of 19 and 30 are $1924$ . It underestimates the number shown by the graph by $76$ calories.

Work Step by Step

Consider the equation as follows: $F=-82{{x}^{2}}+654x+620$ where F represents the number of females and x represents the age group. Now,substitute the value of $x$as 4 and find the value of$F$. $\begin{align} & F=-82{{x}^{2}}+654x+620 \\ & =-82{{\left( 4 \right)}^{2}}+654\left( 4 \right)+620 \\ & =-1312+2616+620 \\ & =1924 \end{align}$ Here, x is considered as 4 because the age group 19-30 lies in the group 4. From the graph, 2000 calories is needed for females of age group19-30. Now, subtract the value of the calorie against age 19 given in the graph from the calculated value of the calorie to obtain: $2000-1924=76$ The value of graph is higher by 76 calories. Hence, the given model underestimates the number shown by the graph by$76$ calories.
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