Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.5 - More on Slope - Exercise Set - Page 227: 30

Answer

The average decrease is approximately $-130$ per year from $2001$ through $2006$.

Work Step by Step

The values of the number of discharges for the year $2001$ is $1273$. The values of the number of discharges for the year $2006$ is $623$. Substitute the values $\left( {{x}_{2}},{{x}_{1}} \right)=\left( 2006,2001 \right)$ and $\left( f\left( {{x}_{2}} \right),f\left( {{x}_{1}} \right) \right)=\left( 623,1273 \right)$ to get the rate of change: $\begin{align} & \frac{\Delta y}{\Delta x}=\frac{f\left( {{x}_{2}} \right)-f\left( {{x}_{1}} \right)}{{{x}_{2}}-{{x}_{1}}} \\ & \frac{\Delta y}{\Delta x}=\frac{623-1273}{2006-2001} \\ & \frac{\Delta y}{\Delta x}=-130 \end{align}$ Therefore, the average rate of change rounded to a whole number from $2001$ through $2006$ is $-130$.
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