Answer
$2710$.
Work Step by Step
1. The geometric series is,
$5000,5000\left( 0.96 \right),5000{{\left( 0.96 \right)}^{2}},\ldots $
The number of fruit files remaining after $15$minutes is provided by the 16th term of the geometric series.
2. Translate the problem into mathematical language or write an equation.
Now, obtain the total files alive in 15 min: ${{a}_{n}}={{a}_{1}}{{r}^{n-1}}$. So,
${{a}_{n}}=5000{{\left( 0.96 \right)}^{16-1}}$
3. Solve
Substitute, ${{a}_{1}}=5000, r=0.96$ and $n=16$,
$\begin{align}
& {{a}_{n}}=5000{{\left( 0.96 \right)}^{16-1}} \\
& =5000{{\left( 0.96 \right)}^{15}} \\
& =5000\left( 0.5421 \right) \\
& \approx 2710
\end{align}$
Thus, there are $2710$ files alive after 15 min.
