derive exponential function from limited information

Can you upload example?

Where we can see input data?

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.

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

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

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)

What's the genesis of the problem?

edit: see below

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

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

       -A-- --B--- ----------------------C----------------------
   1   Area    15% << set this to the desired value (here, 0.15)
   2      k  8.513 << by changing this                          
   3                                                            
   4    x     y                                                 
   5      0   0.00                                              
   6      5   0.41                                              
   7     10   0.86                                              
   8     15   1.37                                              
   9     20   1.92                                              
  10     25   2.55                                              
  11     30   3.25                                              
  12     35   4.05                                              
  13     40   4.97                                              
  14     45   6.03                                              
  15     50   7.27                                              
  16     55   8.75                                              
  17     60  10.53                                              
  18     65  12.72                                              
  19     70  15.47                                              
  20     75  19.05                                              
  21     80  23.89                                              
  22     85  30.78                                              
  23     90  41.39                                              
  24     95  59.85                                              
  25    100 100.00

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)