Answered: When measuring how much change occurs…

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

100%

When measuring how much change occurs in values between two points in time, the
percentage change and average rate of change can help to give context. Keep this in mind as you
answer the following questions.

a. Suppose that Company A and Company B both had their total sales increase by $5000
from the end of 2015 to the end of 2016. However, suppose that Company A had sales
totaling $1 thousand at the end of 2015 and Company B had sales totaling $1 million at
the end of 2015. What was each company’s percentage change in sales from the end of
2015 to the end of 2016? Include units.

b. For which company do you think the increase in sales from 2015 to 2016 had the biggest
impact? Explain.

c. Now suppose that Company A also had their sales increase by $5000 between the end of
2016 and the end of 2021.
What was the company’s average rate of change from the end of 2015 to then end of
2016? What was the company’s average rate of change from the end of 2016 to the end of
2021? Include units with both.

d. During which of these time periods did Company A’s sales increase faster? Explain.

Expert Solution

Step 1: For part a we use the formula ,Percentage Change = [(New Value - Old Value) / Old Value] * 100

(a)
For Company A:
$text Percentage Change end text equals fraction numerator not stretchy left parenthesis straight $ 1 comma 000 plus straight $ 5 comma 000 minus straight $ 1 comma 000 not stretchy right parenthesis over denominator straight $ 1 comma 000 end fraction cross times 100$
$text Percentage Change end text equals fraction numerator not stretchy left parenthesis plus straight $ 5 comma 000 not stretchy right parenthesis over denominator straight $ 1 comma 000 end fraction cross times 100$
$text Percentage Change end text equals 500 straight percent sign$

For Company B:
$text Percentage Change end text equals fraction numerator not stretchy left parenthesis straight $ 1 comma 000 comma 000 plus straight $ 5 comma 000 minus straight $ 1 comma 000 comma 000 not stretchy right parenthesis over denominator straight $ 1 comma 000 comma 000 end fraction cross times 100$
$text Percentage Change end text equals fraction numerator not stretchy left parenthesis plus straight $ 5 comma 000 not stretchy right parenthesis over denominator straight $ 1 comma 000 comma 000 end fraction cross times 100$
$text Percentage Change end text equals 0.5 straight percent sign$