11 The following table shows timber stumpage prices for pine pulpwood in two regions of the American South. Prices are in dollars per ton and were recorded at the start of theindicated year.YearRegion 1 Region 26.604.0020022005 7.506.702007 7.009.00(a) For Region 2, what is the average rate of change per year in price from 2002 to 2005?5.35X(b) Use your answer to part (a) to estimate the price in Region 2 at the start of 2004. (The actual price was $6.40 per ton.)5.35(c) For Region 1, what is the average rate of change per year in price from 2005 to 2007?7.25x(d) Use your answer to part (c) to estimate the price in Region 1 at the start of 2008.7.25X(e) For each region, find the percentage increase in price from 2002 to 2007. (Round your answers to one decimal place.)Region 16.06%Region 2125%(f) On the basis of your answer to part (e), in the absence of other factors, would an investor in timber be better advised to choose Region 1 or Region 2?O Region 1Ⓒ Region 2

Answered: The following table shows timber…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The following table shows timber stumpage prices for pine pulpwood in two regions of the American South. Prices are in dollars per ton and were recorded at the start of the
indicated year.
Year
Region 1 Region 2
6.60
4.00
2002
2005 7.50
6.70
2007 7.00
9.00
(a) For Region 2, what is the average rate of change per year in price from 2002 to 2005?
5.35
X
(b) Use your answer to part (a) to estimate the price in Region 2 at the start of 2004. (The actual price was $6.40 per ton.)
5.35
(c) For Region 1, what is the average rate of change per year in price from 2005 to 2007?
7.25
x
(d) Use your answer to part (c) to estimate the price in Region 1 at the start of 2008.
7.25
X
(e) For each region, find the percentage increase in price from 2002 to 2007. (Round your answers to one decimal place.)
Region 1
6.06
%
Region 2
125
%
(f) On the basis of your answer to part (e), in the absence of other factors, would an investor in timber be better advised to choose Region 1 or Region 2?
O Region 1
Ⓒ Region 2

Expert Solution

Step 1

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What is Average Rate of Change:

The average rate of change is a measure of how quickly on average one quantity changes in relation to another. It provides a general sense of the function's change in value per unit throughout the specified time period. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

Given:

In two regions, the price per ton is given in dollars as:

To Determine:

We determine the average rate of change per year in price per ton in region 1 from 2005 to 2007 and in region 2 from 2002 to 2005. Also, we approximate the price per ton at the beginning of the year 2004.