Answer
The answer is $\$16,384$.
Work Step by Step
The first day $\$1$.
Second day $\$2$.
Third day $\$4$.
The series is $1,2,4,...$ and so on.
This is the geometric series.
Common ratio is $r=2$
The saving on the fifteenth day is
$a_{15}=1\cdot 2^{15-1}$
Simplify.
$a_{15}=1\cdot 2^{14}$
$a_{15}=\$16,384$.
