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1. Simple Exponential Calculation

I need to calculate a growth slowing as the percentage increases.
The ratio is :
60% = +25
120% = +33
180% = +37
240% = +39
300% = +40
Which is the logarithmic equation ?
Thank You!

2. Well your method is actually asymptotic to 41 which means it isn't a logarithm... anyways log would suck because it give negative infinity at 0

What you got there is a very contorted form of f(x) = 1 / c^x OR f(x) = c^-x

Here is what you are looking for:

c - how much to split by every interval... in your case 2 because you are halving every interval

p - this is the base amount you are increasing by... in your case it looks to be 32, because from 60 - 120 you raise 8, 120 - 180 you raise 4, then 2, then 1... so I just multiplied by 2 twice more to get the increase value at 0

i - interval of this increase... in your case .6 or 60%

b - the base value... when x is at the first interval (zero) what is your adjustment up from the p... note how 25 has no logical comparison to the rest of your values. In your case it looks like 9 to coorolate with p properly

x - the percentage value

This equation assumes that 9 is the value you want at 0 (which is twice the increase from 60% - 120%)

anyways:

value = -p * (c ^ -(x / i)) + p + b

or

value = -32 * (2 ^ -(x/.6)) + 32 + 9

what we did:
took the 2^-x

first divide x by the interval i to squeeze the curve horizontally
multiply it by -1 to flip it over
multiply again by p to stretch it vertically for your scale
add on p and b to move it up and put the asymptote where you need it

With some more values thrown in (like 0 position), this equation might change completely... but from what you gave me this is the most logical equation I can see.

3. oh and if you want it to third, or 4th, or anything like that every interval... just change 2 to the reciprocal of the split you want (note 2 is the reciprocal of halfing)

so thirds would be 3
4ths would be 4
etc

4. I think you may use a natural log or the interest rate formula. I will look it up and make a tutorial. I have made one on logarithms.

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