General Question

kingpinlovesyou's avatar

What's the function to show how much percent must you go up to the same point if you went down 1%, 2%, etc?

Asked by kingpinlovesyou (312points) August 12th, 2011

So explain it more in detail.

Imagine a graph, x axis is 1%- 100% and the y axis is how much percent much you go up to reach the same point if you take away the x axis amount? What would the function of the graph be?

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4 Answers

MrItty's avatar

Hmm. An interesting question. Let’s do the math out.

Let W = the original Whole amount
Let X = the percentage to remove (expressed in % form).
Then the new amount N = W – (X * W)= W * (1 – X).
Let Y = the percentage of the new amount N needed to be added to N to get back to W

N + (N * Y) = W
Solve for Y:
N * (1 + Y) = W
1 + Y = W / N
Y = (W / N) – 1

Now express Y in terms of X:

Y = (W / (W * (1 – X) ) – 1

Y = (1 / (1 – X) ) – 1

Plugging a few values into Excel shows that this math does in fact work out. A few sample values:

X = 1% ; Y = 1.010%
X = 5% ; Y = 5.263%
X = 10% ; Y = 11.111%
X = 25% ; Y = 33.333%
X = 50% ; Y = 100%
X = 75% ; Y = 300%
X = 99% ; Y = 9900%
X = 100% Y = [undefined]

LostInParadise's avatar

Same result with a little less algebra.
If x is the percent reduction then the new price is (1-x) of the old one.
To get to the original price, this must be increased by a factor of 1/(1-x).
Subtracting one gives the percent increase 1 – (1/(1-x)).

flutherother's avatar

@LostInParadise Very neat! (but you have written the formula the wrong way round)

Keep_on_running's avatar

…and this was in my “Questions for You” why? :P

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