Answer
$32,768$.
Work Step by Step
Let $a_{n}$ be the number of ancestors after $n$ generations.
$a_{1}=2,$
With each generation, the number of ancestors doubles,
$a_{2}=2\times 2=2^{2}=4,$
$a_{3}=2\times 2^{2}=2^{3}=8,$
$a_{4}=2\times 2^{3}=2^{4}...$
$...$
Common ratio=2, first term=2,
Geometric sequence: $a_{n}=2\cdot 2^{n-1}=2^{n}$
$a_{15}=2^{15}=32,768$.
