derive exponential function from limited information

[cubew00t]

I've been working on a ss that requires me to create a function to determine a value from a exponential curve where the area of the curve is variable . The terminal points, 0,0 and 100,100 remain constant and the curve is symmetrical at the 45degree angle. How can I derive a function knowing only these things.

Here is an image to crudely illustrate what i mean http://i.imgur.com/N2ehO.png

The area can be 10, 20, 35% it doesn't matter, I need a way to determine the function from just the area! Thank you!

[zbor]

Can you upload example?

Where we can see input data?

[cubew00t]

The only thing I'm inputting is the area under the curve. What I need is a way to generate the function.

[shg]

The terminal points, 0,0 and 100,100 remain constant

The value of the exponential function y = m * b ^ x has a value of m at x = 0, not 0.

EDIT: And an exponential is not symmetric in that fashion.

[zbor]

This more looks like shifted y=a/x to me

[cubew00t]

i can see you are correct in that it is not an exponential function, http://i.imgur.com/dcSw0.png this is more of what i was going for.. is there a way to express this in excel?

[shg]

There would be if you knew what the type of the function is.

[zbor]

How about instead of function make aproximation with two lines?

First one will go from 0 to (1-p)*100
And second from (1-p)*100 to 100

Formula for first part is a*X
And second 100+(x-100)/a

Where a is p/(1-p) and p is needed percentage (i.e. 0,15)

[cubew00t]

could they be parabola tilted at a 45 degree angle?

[shg]

What's the genesis of the problem?

[cubew00t]

edit: see below

[cubew00t]

Ok, it seems as though I need more information.

http://i.imgur.com/qCnFL.jpg

I need to create a function in excel for a hyperbola and the only information I have is the area. If I input a certain area, it would ideally generate a new function that covers more or less area but still goes through 0,0 and 100,100.

Thank you!

[shg]

I'm happy to help if you're done with the other forum, otherwise please continue there.

[cubew00t]

Yes, I'm done. Thank you.

[shg]

It would be very messy to solve for k as a function of area in closed form. You could use Solver:

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The formula in B1 is =(k * (100+k) * LN((100+k) / k) - 100*k) / (100 * 100)

The formula in B5 and copied down is =k * x / (100 - x + k)

[cubew00t]

"The formula in B1 is =(k * (100+k) * LN((100+k) / k) - 100*k) / (100 * 100)"

That's just what I needed. Can you explain how to reverse this equation so I can input a value for B1(area) and generate a value for k?

[shg]

That's a very hard formula to invert, and why I suggested you use Solver.