The population of the region is decreasing according to the formula $y=y_{0} e^{-0.0256 t}$. In this formula, $t$ is time in years and $y_{0}$ is the initial population at time 0 . If the size of the population in 2000 was 11,838 , use the formula to predict the population of the region in the year 2014. In year 2014 the population of the region will be approximately (Round to the nearest whole number as needed.)

Step 1 ：The problem is asking us to predict the population of a region in the year 2014 given that the population in 2000 was 11,838 and the population decreases according to the formula \(y=y_{0} e^{-0.0256 t}\).

Step 2 ：We know that \(y_{0}\) is the initial population at time 0, which in this case is the population in 2000, and \(t\) is the time in years.

Step 3 ：So, we need to find the value of \(y\) when \(t = 2014 - 2000 = 14\) years and \(y_{0} = 11,838\).

Step 4 ：Substitute \(y_{0} = 11838\) and \(t = 14\) into the formula, we get \(y = 11838 * e^{-0.0256 * 14}\).

Step 5 ：Calculate the value of \(y\), we get \(y = 8272.31747306438\).

Step 6 ：Round \(y\) to the nearest whole number, we get \(y = 8272\).

Step 7 ：Final Answer: The population of the region in the year 2014 will be approximately \(\boxed{8272}\).