Derivation of x=0.779

In the equation

where

M_o=Initial mass of ungelatinized starch
M_t=Mass of ungelatinized starch at time t
M_f=Mass of ungelatinized starch at final time

If we divide the top and bottom of the above fraction by the total mass of starch present, M, we get:

Initially, when the potato is raw, 23% of the starch in it is amorphous. That means

From the literature search, it was found that the highest percentage of starch that was gelatinized was 96.2%. That means

So now we have

The potato is said to be cooked when 80% of the starch in the center has been gelatinized. That means:

So the potato is cooked when: