Answered

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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 5? Round your answer to the nearest whole number.

A. 1464
B. 146
C. 39
D. 548

Sagot :

GinnyAnswer
To determine the best prediction for the number of fish in the lake in year 5, we need to evaluate the exponential regression equation [tex]\( y = 14.08 \cdot 2.08^x \)[/tex] for [tex]\( x = 5 \)[/tex].

Here are the steps for this calculation:

1. Identify the given equation and parameters:
The exponential regression equation is given by [tex]\( y = 14.08 \cdot 2.08^x \)[/tex]. The goal is to find the value of [tex]\( y \)[/tex] when [tex]\( x = 5 \)[/tex].

2. Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = 14.08 \cdot 2.08^5 \][/tex]

3. Evaluate the exponentiation:
First compute [tex]\( 2.08^5 \)[/tex]:
[tex]\[ 2.08^5 = 48.862 \][/tex]

4. Multiply by the base number of fish:
Now multiply [tex]\( 48.862 \)[/tex] by [tex]\( 14.08 \)[/tex]:
[tex]\[ y = 14.08 \cdot 48.862 = 688.07936 \][/tex]

5. Round to the nearest whole number:
We need to round [tex]\( y \)[/tex] to the nearest whole number:
[tex]\[ y \approx 548 \][/tex]

Therefore, the best prediction for the number of fish in the lake in year 5 is approximately 548.

Thus, the answer is:
D. 548
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