andieliz523 said:
I have to find an algebreic equation/rule for this In/Out table. For example, the equation might be y=3x+4. It has to be like this. It CANNOT be something like you multiple by one more than you did with the previous number. IT MUST BE AN EQUATION.
In= 5, 6, 8, 10, 12
Out= 61, 75, 100, 125, 150
andieliz523,
what I was looking for was to see if the second numbers are a multiple of the first numbers, respectively,
except that there may be a deviation from this by addition or subtraction by a constant.
I saw this:
\(\displaystyle 5(12) + 1 = 61\)
\(\displaystyle 6(12) + 3 = 75\)
\(\displaystyle 8(12) + 4 = 100\)
\(\displaystyle 10(12) + 5 = 125\)
\(\displaystyle 12(12) + 6 = 150\)
The \(\displaystyle 61\) in the "Out" list is not consistent for a "reasonable" pattern,
based on your expected level of math.
I would challenge that either the "61" is supposed to be"62" and was copied incorrectly in class or from a
textbook/handout, that the instructor wrote it wrong, or that it is an error in a textbook or handout.
Because you want a rule, a function, then that equation of straight line by galactus would not work
because it approximates.
The pattern shown in my table is that the output drops by 25 for each drop by 2 for the multiplier of 12.
Or for three consecutive entries, the output in the middle is the average of the smaller and larger
outputs, while the corresponding multiplier on 12 is the average of the two multipliers above and below
it. Also, the number being added to the product of the multipler and 12 is half of the multiplier.
Either the first numbers should be changed to refect this:
\(\displaystyle 4(12) + 2 = 50\)
\(\displaystyle 6(12) + 3 = 75\)
\(\displaystyle 8(12) + 4 = 100\)
\(\displaystyle 10(12) + 5 = 125\)
\(\displaystyle 12(12) + 6 = 150\)
Or the first numbers should be changed to:
\(\displaystyle 5(12) + 2.5 = 62.5\)
\(\displaystyle 6(12) + 3 = 75\)
\(\displaystyle 8(12) + 4 = 100\)
\(\displaystyle 10(12) + 5 = 125\)
\(\displaystyle 12(12) + 6 = 150\)
--------------------------------------------------------------
Suppose \(\displaystyle n\) is a nonnegative integer.
I am thinking \(\displaystyle 2(n + 1)(12) + (n + 1) =\)
\(\displaystyle 24n + 24 + n + 1 =\)
\(\displaystyle 25n + 25\)
But instead of the "In" values being 1, 2, 3, 4, ..., they (would be) 4, 6, 8, 10, 12... \(\displaystyle **\)
To get numbers from the first list in \(\displaystyle **\), you could subtract 2 from the corresponding numbers from the
second list in \(\displaystyle **\), and then divide that result by 2.
Example:
\(\displaystyle (8 - 2)/2 = 3\)
Then \(\displaystyle 8\) from the "In" list is the \(\displaystyle 3^{rd}\) number in the "Out" list.
Replace \(\displaystyle n\) with \(\displaystyle \frac{x - 2}{2}.\)
Then \(\displaystyle y = 25(\frac{x - 2}{2}) + 25\)
\(\displaystyle y = 12.5x - 25 + 25\)
\(\displaystyle \boxed{y = 12.5x}\) . . . . \(\displaystyle \ \ If \ the \ list \ were \ to \ be \ different.\)
Examples:
For \(\displaystyle x = 5, y = 12.5(5) = 62.5\)
For \(\displaystyle x = 8. y = 12.5(8) = 100\)
Here is a quicker observation:
For all of the "in" values in your list greater than \(\displaystyle 5,\) the "Out" value is exactly
\(\displaystyle 12.5\) times its corresponding "In" value. So, for a linear function, the first "Out" value
should be changed, or both the first "In" and "Out" values should be changed.
