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Can you help? If $0.6 = 10$ and $30 = 1$, what does $3.3$ equal and what does $1.62$ equal? Is there a formula to this and if so what is it, please? This would enable me to calculate any number between $0.60$ and $30.00$ (to two decimal places) and correlate it to a number between $10$ and $1$ (to one decimal place).

Thank you,

Steve

Mr. Brooks
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Steve B
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  • There are lots of functions which can accomplish this. Do you want it to seem "fair"? Should it be exponential? – abiessu Nov 05 '15 at 04:28
  • Thanks for questions. "fair" sounds good, what would it look like? – Steve B Nov 05 '15 at 04:31
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    Maybe you can try giving a few more values that suit what sort of function you are thinking about? – Element118 Nov 05 '15 at 04:43
  • The answer depends on the relation between input and output values. You provided two points of a graph. The easiest is a straight line between both points. – mvw Nov 05 '15 at 04:50
  • Its difficult ti give a few more values at this stage. Though I'm thinking that this might be exponential after all. If we just look at the starting point and the end point. input 30.00=1 and input 0.60=10, if it is exponential what would inputs 3.3 and 1.62 look like, as examples? – Steve B Nov 05 '15 at 05:48

1 Answers1

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Sure. This is easily done if you want a linear relationship. If you want a linear relationship, you could use the (approximate) formula $$\text{index}=-.306*\text{value}+10.18$$

Thus, you could plug in 3.3 and see that it would give you about 9.17 $$9.17\approx(-.306)(3.3)+10.18$$

However, it should be noted, a linear relationship is just one example of how you could do this. Like, those final few tenths as you near 0.6 could be more valuable than those near 30 (on the input).

EDITING TO ADD:So, reading your comments, there's really no "correct" answer. Just depends on your tastes. But here's one you could play around with and see if it gives reasonable answers. $$y=\frac{5x+22}{5x-\frac{1}{2}}$$

Where $x$ is your input $(0.6\text{ or }30)$ and $y$ is your index $(10\text{ or }1)$ enter image description here

turkeyhundt
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  • Hi, you are correct, the most critical area is between 0.6 and 5. – Steve B Nov 05 '15 at 04:36
  • Then it's not so simple. You need to decide how you want the curve to look. Logarithmic, exponential, quadratic are some examples. Also, is 0.6 the lowest input? Do you need an index for 0.5? – turkeyhundt Nov 05 '15 at 04:37
  • Hi, this is challenging for me with just high school maths a very long time ago. – Steve B Nov 05 '15 at 04:41
  • Oops i keep hitting enter for the next line! Unfortunately at this stage i have only a small amount data to use. Yes 0.6 is the lowest, that or lower is 10 out 10. Its quite difficult to achieve. Most scores are between 10 and 20 so just average – Steve B Nov 05 '15 at 04:48
  • I'll need to play with this in Excel to get to understand it better. Your guidance is much appreciated. May i come back to you if i have anther question about this? – Steve B Nov 05 '15 at 05:27
  • Its difficult ti give a few more values at this stage. I'm thinking that this might be exponential after all. If we just look at the starting point and the end point. input 30.00=1 and input 0.60=10, if it is exponential what would inputs 3.3 and 1.62 look like, as examples? – Steve B Nov 05 '15 at 05:51