Interview Trap Riddle : Hungry Worm & Old Tree

A very hungry worm reaches a tree covered in a lot of leaves. The worm eats 1 leaf and goes away.

On the next day... i.e. day 2..., the worm reaches the tree again and this time it eats twice the number of leaves it ate on the previous day... so it eats 2 leaves on the 2nd day...
On day 3, it eats 4 leaves....
On day 4.. it eats 8 leaves...
and so on..

On Day 30.... it eats the corresponding number of leaves for this day.
And all the leaves on the tree are finished on this day.

RIDDLE :
On which day did the worm finish exactly half of the total number of leaves ?

This riddle has a great analogy to a popular 'Lotus in a pond' riddle. But you should be alert while solving this riddle becuase it has a very tricky answer.
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