Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ
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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
.