Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 245: 63

Answer

(a) $f(x)=622.25x+22036$. See graph and explanations. (b) $23903$ dollars. (c) $f(x)=653x+21634$

Work Step by Step

(a) To find the linear function $f(x)=ax+b$, use the data points $(0,22036)$ and $(4,24525)$, we have $a=\frac{24525-22036}{4-0}=622.25$. Use the first point, we have $b=22036$, thus we have $f(x)=622.25x+22036$. See graph. The slope of the graph indicates the average increase of tuition fees per year from 2009 to 2013. (b) For year 2012, we have $x=2012-2009=3$ and $f(3)=622.25(3)+22036=23902.75\approx23903$ dollars. Compare to the actual value of $23460$, the prediction is close. (c) Use the linear regression feature of a graphing calculator, we can find the equation of the line of best fit as $f(x)=653x+21634$
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