Answer:
$16,384
Explanation:
Let's find the general equation for his savings:
The first day he saves $1 =
The second day, $2 = 1*2 =

The third day, $4 = 1*2*2 =
The fourth day, $8 = 1*2*2*2 =

In general, in the n-th day, he saves

With this, we can calculate the amount that he will save on the fifteenth day: