what equation describes this trend?

[dragonstar57]

x=1 y=25%

x=2 y=40%

x=3 y=50%

x=4 y=57%

x=5 y=62%

x=6 y=66.60%

this is based upon how 1/4=25 2/5=40

each time the numerator and denominator both increase by one.

but I can't figure out the equation!

Edited September 3, 2010 by cipher510

[Shadow]

I don't think this can be described by a (non-piecewise) equation, unless the last three percentages are 57.1429..., 62.5 and 66.666... . If that is indeed the case (which it should be according to the relationship you gave at the end), it isn't very difficult to find the equation. For starters, can you write down the general form of the fractions 1/4, 2/5, 3/6 etc. ? (for example, the general form of the fractions 1/2, 2/3, 3/4 etc. would be [math]\frac{x}{x+1}[/math]).

Edited September 3, 2010 by Shadow

[dragonstar57]

yes the numbers were rounded to the nearest whole number

how would that be done?

oder of operations tells me to divide so i get

3

___=1.3 repeated

3+1

 

or if I add first

3

___

3+1

 

3

___=.75

4

so what am I doing wrong?

someone on yahoo said y = x/(x + 3) but that doesn't seem to work either

Edited September 3, 2010 by cipher510

[ewmon]

(an alternate method)

 

Easy...let your computer figure it out for you.

 

If you're lazy like me...

 

1. Copy and paste all six lines of data into a Word document and replace (Ctrl+H) " y" with "^ty".

 

2. Then copy and paste into an Excel spreadsheet (the tabs are required for the data to fill two columns).

 

3. Highlight the data again, and select Insert/Chart... and choose the XY (Scatter) chart type.

 

4. Right click on a data point on the chart and select Add Trendline...

 

5. Choose a type of trendline and, under the Options tab, select Display equation on chart as well as Display R-squared value on chart

 

6. Do this for all the types of trendlines, monitoring their R² values.

 

7. Record the trendline type, equation and R² for which the R² value is the highest.

 

Note: A very good fit should be very close to 1, at least greater than 0.98 or so.

 

Come back to the forum with your answer, and let's compare results.

[Shadow]

If you just want someone else to do the thinking for you, practically everyone here can give you the correct answer, or you can use WolframAlpha, which is much quicker and easier to use than Excel. But I think you should try and figure out the answer by yourself if you can, it's good practice.

Now, I'm not sure what you're doing in those two divisions; it seem that in the first case, you somehow mistook [math]\frac{3}{3+1}[/math] for [math]\frac{3 + 1}{3}[/math]. There is a very big difference between the two, and it is not arbitrary which way you choose to evaluate the fraction. True, the precedence rule states that division should be performed before addition. But the mistake you made was dividing three by three, when in fact you were supposed to divide three by three plus one. Now, since you can hardly divide a number by two other number and a mathematical operation all in one, you first have to evaluate 3 + 1 = 4; thus, [math]\frac{3}{3+1} = \frac{3}{4} = 0.75[/math].

 

The person(s) on Yahoo! were correct, but again, you're letting other people do the work for you. Focus on the question I asked previously; can you write down the general form of the fractions [math]\frac{1}{4}, \frac{2}{5}, \frac{3}{6}...[/math]? Here are a couple of hints at how to arrive at the solution:

 

Analyze the fractions you have in front of you. Note that if the numerator is one, the denominator is four, which is one plus three. If the numerator is two, the denominator is five, which is two plus three, if the numerator is three the denominator is six, which is three plus three and so on. Can you find a rule for how the fractions are generated?

 

Ask yourself, if the numerator were four, what would the denominator be? If the numerator were five, what would the denominator be?

 

Finally, ask yourself, if the numerator were some number [math]x[/math], what would the denominator be? Or, and I'm almost telling you the answer here, how much bigger would the denominator be?

 

Hope this helps.

 

PS.: If you can describe the rule using English but not using math, do so, and we'll work from there.

Edited September 4, 2010 by Shadow

[dragonstar57]

y=x/(x+3)

the (x+3) finds the numerator (the # on the bottom )

you divide by x which is the denominator (the # on top)

y=3/(3+3)

y=3/(6)

y=0.5

which is = to 0.50

which is = to 50%?

is this right?

Edited September 4, 2010 by cipher510

[Shadow]

Very good. Now, we have the general form of the fraction, but that only gives us numbers smaller than one, while we want number in the range <0, 100> (or equivalently, percent). So, instead of getting 0.5, we want 50. Instead of getting 0.625 we want to get 62.5. Try altering the general from so it gives these results.

[dragonstar57]

y=(x/(x+3)*100?

[Shadow]

There you go. That's the equation you were looking for.

[dragonstar57]

thank you for your help

[the tree]

Except it should just be x/(x+3).

[Shadow]

Why?

[the tree]

Because 1/4*100=2500%, and you're looking for 25%.

[Shadow]

I see what you mean. The multiplycation by 100 in my version was an attempt to convert to percent directly, as in the OP. If I added the percent sign, as in [math]\frac{x}{x+3} * 100 \%[/math], would it then be correct?

Edited September 7, 2010 by Shadow

[the tree]

Yes.

[dragonstar57]

I don't see what you mean 1/4*100=25

http://www.google.com/search?hl=en&source=hp&biw=1024&bih=653&q=1/4*100&aq=f&aqi=g10&aql=&oq=&gs_rfai=C6rOxPmqeTI7uFZiQoATJ8ZyHCwAAAKoEBU_QL8ya

thus converting the decimal answer in to a percentage

Edited September 25, 2010 by cipher510

[Shadow]

Careful; the mistake I made is the same you just made; [math] 25 \neq 25\%[/math]. Think of the percent sign as a unit, like in physics.

Edited September 26, 2010 by Shadow

[dragonstar57]

oh its that simple? i just left off the %?

isn't that not even worth mentioning?

Edited September 26, 2010 by cipher510

[insane_alien]

isn't that not even worth mentioning?

 

tell that to the people who were on board the gimli glider.

 

units are VERY worth being VERY explicit about.

 

for instance, if you went to a bank and the offered you an account with 2 interest, how do you know if its good or not? it could be 2% per year or it could be 2% per millenium or it could even be 2 kiwi fruits total.

 

if you think units don't matter then please never enter a career path that involves mathematics in any way shape or form.

[dragonstar57]

tell that to the people who were on board the gimli glider.

 

units are VERY worth being VERY explicit about.

 

for instance, if you went to a bank and the offered you an account with 2 interest, how do you know if its good or not? it could be 2% per year or it could be 2% per millenium or it could even be 2 kiwi fruits total.

 

if you think units don't matter then please never enter a career path that involves mathematics in any way shape or form.

???gimli glider??? what that?

I just meant that the conversion of a fraction into a decimal is to multiply by 100

and ad on the % but if you multiply times 100% you get the same answer

and i'm going into cryptography aka a whole lot of math

Edited September 26, 2010 by cipher510