Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.3 - Polynomial Functions and Their Graphs - Exercise Set - Page 350: 74


a. $26747$, point $(10,26747)$ b. underestimates by 1253. c. rises to the right, useful to some extent.

Work Step by Step

a. For $x=10$, with the given function, we have $f(10)=0.76(10)^3-30(10)^2-882(10)+37807=26747$ This means that the value from the model equation is 26747 for year $1970+10=1980$. The point is at $(10,26747)$ on the right graph. b. From the bar graph, we have $28000$ for year 1980. Thus the above value underestimates the actual data by 1253. c. The leading term is $0.76x^3$, with a coefficient of $+0.76$ and odd power. Thus the end behavior to the right is that $x\to\infty, y\to\infty$ -- that is, the curve will rise to the right. This function models the population from year $1970$ to $2010$ fairly accurately with the population decreasing initially and rising after $x=35$ or year $2005$ as a result of the conservation efforts. Thus, it is useful to some extent.
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