Pregunta
The number of fish in a lake can be modeled by the exponential regression equation \( y=14.08 \cdot 2.08^{x} \), where \( x \) 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. 81 B. 1758 C. 1140 D. 176
Ask by Collins Norris. in the United States
Mar 01,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The best prediction for the number of fish in year 6 is 1140.
Solución
We are given the equation y = 14.08 · 2.08^x, and we need to predict the number of fish when x = 6.
Step 1. Substitute x = 6:
y = 14.08 · 2.08^6
Step 2. Calculate 2.08^6:
A rough calculation gives 2.08^6 ≈ 81.3
Step 3. Multiply by 14.08:
y ≈ 14.08 · 81.3 ≈ 1145
Rounded to the nearest whole number, this is about 1140 fish.
Thus, the best prediction is 1140, which corresponds to option C.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Beyond the Answer
To find the number of fish in year 6, substitute \( x = 6 \) into the equation: \[ y = 14.08 \cdot 2.08^{6} \] Calculating \( 2.08^{6} \): \[ 2.08^{6} \approx 64.82 \quad \text{(rounded)} \] Now substitute back into the equation: \[ y \approx 14.08 \cdot 64.82 \approx 911.7 \] Rounded to the nearest whole number, we have approximately 912 fish. From the options provided, the best prediction is **C. 1140**, as it is the closest available option.
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