To determine the best prediction for the number of fish in the lake in year 6 using the given exponential regression equation [tex]\(y = 14.08 \cdot 2.08^x\)[/tex], we will follow these steps:
1. Identify the parameters:
- Initial value (when [tex]\(x = 0\)[/tex]): 14.08
- Growth rate: 2.08
- Year ([tex]\(x\)[/tex]): 6
2. Substitute the year into the equation:
Substitute [tex]\(x = 6\)[/tex] into the exponential regression equation:
[tex]\[
y = 14.08 \cdot 2.08^6
\][/tex]
3. Evaluate the exponent:
Compute [tex]\(2.08^6\)[/tex].
4. Multiply by the initial value:
Multiply the computed power by 14.08:
[tex]\[
y = 14.08 \cdot (2.08^6)
\][/tex]
5. Round to the nearest whole number:
Finally, round the result to the nearest whole number for the predicted number of fish.
After following these steps, the calculation yields a result of 1140 when rounded to the nearest whole number.
Therefore, the best prediction for the number of fish in year 6 is [tex]\(\boxed{1140}\)[/tex].
