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So suppose in the news you hear tuition is expected to increase 7% next year.
If tuition this year was $1,200 per quarter, what will be next year?
So there is couple of ways we can think about this.
One way would be to say that if we're going to add an additional 7% on top of
the tuition the next year. Next year will be our original 100% plus
an extra 0.07%, or in other words, 107% of this year.
So in other words our tuition this year was $1200, let's find 107% of that $1200.
And, of course, usually we don't actually multiply it by the percent, we go ahead
and rewrite it as a decimal. We go ahead and multiply, we come up with
next year's tuition will be $1,284 per oops, per quarter.
Now, another way we could have done this would be to say that 7% of 1,200.
In other words, we could have started by just figuring out what the increase was
going to be, so we could have said $1,200 times 7% is $84.
In other words, the tuition is going to increase by $84 and then the tuition this
year plus the increase gives us the expected tuition for next year, and that
been another way to approach the same problem.
And here is another problem the value of a car dropped from 7400 to a hundred
dollars to $6800 over the last year. What percent decrease is this?
So let's figure out, first off, how much the actual value decreased.
If we take the new price minus the old price, we see that the price dropped by
$600, so a $600 decrease. Now, usually when we talk about changes,
it's easiest to talk about the absolute value of the change, which in this case
would be $600. And we call this an absolute change, this
is the actual change in absolute value, the actual change from one year to the
next so it is $600 decrease. But we're really interested in the
percent change and so we need to take this out of the starting amount.
Now, this is really important when we talk about changes, relative changes, we
need the, the absolute change. The absolute change divided by the
starting quantity. So our change was 600 but that needs to
be relative to our starting quantity. In this case we dropped from 6, 7,400, so
it makes sense to count 7,400. As what we call the base of our percent?
Now, base ends up being really important, and we'll see later.
But for now we'll just say 600 out of 7400, if we divided that we would get
0.081, which is an 8.1% decrease. And again, this is what we call a
relative change. And absolute changes and relative changes
are two different ways to describe how somethings changed, and both have their
value. often times though, the relative change
is more useful to see sort of help big of a change it is because it describes that
change relative to the starting at point.