[Math] pastebin-like services and logarithmic scale

Couple of pastebin-like services has a file retention period rule, which is calculated like:

FILE RETENTION PERIOD
---------------------

retention = min_age + (-max_age + min_age) * pow((file_size / max_size - 1), 3)

   days
    365 |  \
        |   \
        |    \
        |     \
        |      \
        |       \
        |        ..
        |          \
  197.5 | ----------..-------------------------------------------
        |             ..
        |               \
        |                ..
        |                  ...
        |                     ..
        |                       ...
        |                          ....
        |                              ......
     30 |                                    ....................
          0                      256.0                      512.0
                                                              MiB

( https://0x0.st/ )

Files are kept for a minimum of 3, and a maximum of 100 Days.

How long a file is kept depends on its size. Larger files are deleted earlier 
than small ones. This relation is non-linear and skewed in favour of small 
files.

The exact formula for determining the maximum age for a file is:

MIN_AGE + (MAX_AGE - MIN_AGE) * (1-(FILE_SIZE/MAX_SIZE))^2

( https://x0.at/ )

The graph on first example is more steep, due to cubic function used. The second example is less steep: square function used instead.

I recreated the plot of first example in Wolfram Mathematica (square):

The second example (cubic):

Can you solve this problem without log scale? I don't even know how.

Also, my Wolfram Mathematica notebook in HTML form

And the notebook

(the post first published at 20231031.)

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