Question 86352: ) Business and finance. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
Found 4 solutions by checkley75, venugopalramana, ikleyn, KMST:
Answer by checkley75(3666)   (Show Source):
Answer by venugopalramana(3286)  (Show Source):
You can put this solution on YOUR website! ) Business and finance. The electricity costs of a business decreased from $12,000 one year to $10,920 the next. What is the rate of decrease?
ORGL=12000
AFTER 1 YEAR =10920
DECREASE = 12000-10920=1080
RATE OF DECREASE =1080/10920 = 0.0989...OR....9.89%
Answer by ikleyn(54062)  (Show Source):
You can put this solution on YOUR website! .
The electricity costs of a business decreased from $12,000 one year to $10,920 the next.
What is the rate of decrease?
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The solution in the post by @venugopalramana is incorrect,
since the base for comparison is taken incorrectly there.
Below is my correct solution.
The base value is $12,000. <<<===--- this is the base value to compare with (!)
The next year's value is $10,920.
The decrease is 12000 - 10920 = 1080 dollars.
The rate of decrease is  = 0.09.
ANSWER. The rate of decrease is 0.09, or 9%.
Solved correctly.
In such problems, if the opposite is not stated explicitly, the base for comparison is ALWAYS the starting value,
and the rate of increase or decrease should be calculated relative to this value, by default.
It is the BASIC RULE in such kinds of problems,
and it is the BASIC RULE to memorize and to use.
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In her post, the respected tutor @KMST shared her thoughts regarding the use of the term "rate of decrease"
in the problem. For my part, I would like to state that using this term in such school problems is absolutely correct, standard,
and generally accepted. I clearly remember how we, my generation, were taught this in school
some 65 - 70 years ago.
Our school curricula may have differed. What I do remember well is that my mathematics curriculum was perfectly
structured, the Math textbooks were ideally written, and the teachers were knowledgeable and caring.
It was a matter of professional honor for them to teach us correctly.
Different problems (across various areas) of school mathematics have their own conventions regarding terminology.
Learning mathematics involves not only mastering algorithms but also learning the rules of word usage — that is,
standard terminology. In this specific case (in this particular problem), the use of terms is entirely correct.
Usage might differ in other fields (such as calculus), but that is part of the instruction specific to those respective
topics.
(My generation is "boomers", the "sputnik" era, with the school and university years 1954-1970,
when the methodology of teaching school Math was at its highest level).
/ / / / / / / / / / / / / / / /
An interesting idea came to my mind.
Euclid’s volumes served as the source of knowledge in geometry. They were the ultimate authority
from the very early age of written mathematics and remained so for centuries; there were no other sources
of comparable standing. Not only was his axiomatic system perfect; not only was the logical structure
of the course unsurpassed - his mathematical prose was excellent, too.
Thanks to this, Geometry endured as a school subject for centuries and even millennia.
Throughout these years and centuries, Geometry was not merely a school subject, but a means, a tool
of developing, honing, and sustaining human intellect.
But then other authors appeared; a multitude of authors and textbooks emerged — and what happened?
The standard of mathematical exposition declined; school geometry texts ceased to engage students,
and Geometry was practically eliminated from the school curriculum—with near-total public consensus.
The culture of geometric proofs and problem-solving vanished, and today it survives in its traditional form
only "underground"—in the minds of enthusiasts.
Answer by KMST(5484)  (Show Source):
You can put this solution on YOUR website! I "rate" this question as a very poorly worded question for an simple situation,
presented as an arithmetic problem.
Nowhere in the question I see a request for percentage of decrease.
I understand that when talking about interest, among people in business and finance,
the word "rate" is often shorthand for relative rate of change,
expressed as percentage, omitting the variable, with the assumption that
the "other details" are understood by all
(the sign of the change, the variable, and the continuous compounding, or compounding period).
I would not expect that students faced with this problem would not be experts in calculus or finance.
They may not realize or care much about how the "rate" is calculated on their debts and savings.
They may not even understand the difference between entering into their calculator (1200-10920)/12000 and entering 12000-10920/12000.
In my book, rate is  for the change in some function,
calculated as average over some period,
or maybe there could be an instant rate  for one value of  or as a function of , with not necessarily be time.
What is the function here?
If the function is cost of electricity as a function of calendar or fiscal year (or whatever they refer to as one year and the next one),
the average yearly rate of change (in $/year) is
 ,
and the average yearly rate of decrease (in $/year) would be 1080.
If they asked for relative rate of decrease, it would be 9% per year.
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