The number of fish in a lake can be modeled by the exponential regression equation [tex]y = 14.08 \cdot 2.08^x[/tex], where [tex]x[/tex] represents the year.

Which is the best prediction for the number of fish in year 6? Round your answer to the nearest whole number.

A. 1758
B. 176
C. 81
D. 1140



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]