To predict the number of fish in the lake in year 7 using the exponential regression equation [tex]\( y = 14.08 \cdot 2.08^x \)[/tex], follow these steps:
1. Identify the given function:
[tex]\[
y = 14.08 \cdot 2.08^x
\][/tex]
Here, [tex]\( y \)[/tex] represents the population of fish, [tex]\( 14.08 \)[/tex] is the initial population, [tex]\( 2.08 \)[/tex] is the growth rate, and [tex]\( x \)[/tex] is the year.
2. Plug in the value for the year [tex]\( x = 7 \)[/tex]:
[tex]\[
y = 14.08 \cdot 2.08^7
\][/tex]
3. Calculate [tex]\( 2.08^7 \)[/tex]:
[tex]\[
2.08^7 \approx 168.378
\][/tex]
4. Multiply the initial population by this result:
[tex]\[
y = 14.08 \cdot 168.378 \approx 2371.62488981
\][/tex]
5. Round the result to the nearest whole number:
[tex]\[
2371.62488981 \rightarrow 2372
\][/tex]
Therefore, the best prediction for the number of fish in year 7, rounded to the nearest whole number, is:
[tex]\[
\boxed{2372}
\][/tex]
Thus, the correct answer is:
B. 2372
