Answer
On\[{{15}^{th}}\] day the person puts aside\[\$16,384\].
Work Step by Step
: The provided information can be modelled as a geometric progression with the following parameters:
\[a=1,\,r=2,\,n=15\]
The fifteenth term is,
\[\begin{align}
& {{a}_{n}}=a{{r}^{n-1}} \\
& {{a}_{15}}=1\times {{2}^{\left( 15-1 \right)}} \\
& ={{2}^{14}} \\
& =16384
\end{align}\]
Hence, on\[{{15}^{th}}\] day the person puts aside\[\$16,384\].
