A rare first-edition book is currently priced at $200. After one year, the price of the book is anticipated to be 1.15 times the
current price of the book. Then, one year after that, the price of the book is anticipated to be 1.15 times the price of the book the previous year. If this pattern continues, which of the following graphs represents the price of the book over time?
A. Graph W
B. Graph X
C. Graph Y
D. Graph X
A. Graph W
B. Graph X
C. Graph Y
D. Graph X
2 answers:
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Answer:
Possible answer: .
Step-by-step explanation:
Rewrite the bounds of as fractions:
The simplest fraction for is
. Write the upper bound
as a fraction with the same denominator:
.
Hence the range for would be:
.
If the denominator of is also
, then the range for its numerator (call it
) would be
. Apparently, no whole number could fit into this interval. The reason is that the interval is open, and the difference between the bounds is less than
.
To solve this problem, consider scaling up the denominator. To make sure that the numerator of the bounds are still whole numbers, multiply both the numerator and the denominator by a whole number (for example, 2.)
.
.
At this point, the difference between the numerators is now . That allows a number (
in this case) to fit between the bounds. However,
can't be written as finite decimals.
Try multiplying the numerator and the denominator by a different number.
.
.
.
.
.
.
It is important to note that some expressions for can be simplified. For example,
because of the common factor
.
Apparently works.
while
.