Question

2 ice cubes of exact equal size/weight. One is heated at 100 deg and the other at 50 deg. Do each melt individually at the same speed each or do they each exponentially melt fast as the ice gets smaller?

Answer 1

The power dlivered to the cubes is proportional to

$$P\backsim \frac{A}{V}\backsim \frac{a^2}{a^3}=\frac{1}{a}$$

That's why, they each exponentially melt fast as the ice gets smaller.