Answer :
To predict the number of fish in the lake in year 6 using the given exponential regression equation \( y = 14.08 \cdot 2.08^x \), follow these steps:
1. Identify the given equation and value of \( x \):
[tex]\[ y = 14.08 \cdot 2.08^x \][/tex]
Here, \( x \) represents the year. We are interested in the number of fish in year 6, so \( x = 6 \).
2. Substitute \( x = 6 \) into the equation:
[tex]\[ y = 14.08 \cdot 2.08^6 \][/tex]
3. Calculate \( 2.08^6 \):
[tex]\[ 2.08^6 \approx 81.00028425 \][/tex]
4. Multiply this result by the base value 14.08:
[tex]\[ y = 14.08 \cdot 81.00028425 \approx 1140.2042739471158 \][/tex]
5. Round the calculated number of fish to the nearest whole number:
[tex]\[ 1140.2042739471158 \approx 1140 \][/tex]
Thus, the best prediction for the number of fish in year 6, rounded to the nearest whole number, is 1140.
Therefore, the correct answer is:
[tex]\[ \boxed{1140} \][/tex]
1. Identify the given equation and value of \( x \):
[tex]\[ y = 14.08 \cdot 2.08^x \][/tex]
Here, \( x \) represents the year. We are interested in the number of fish in year 6, so \( x = 6 \).
2. Substitute \( x = 6 \) into the equation:
[tex]\[ y = 14.08 \cdot 2.08^6 \][/tex]
3. Calculate \( 2.08^6 \):
[tex]\[ 2.08^6 \approx 81.00028425 \][/tex]
4. Multiply this result by the base value 14.08:
[tex]\[ y = 14.08 \cdot 81.00028425 \approx 1140.2042739471158 \][/tex]
5. Round the calculated number of fish to the nearest whole number:
[tex]\[ 1140.2042739471158 \approx 1140 \][/tex]
Thus, the best prediction for the number of fish in year 6, rounded to the nearest whole number, is 1140.
Therefore, the correct answer is:
[tex]\[ \boxed{1140} \][/tex]
