Question

data about the sound levels from a new speaker are collected at a manufacturing facility and are used to calculate the model \\(\hat{y} = 62.7(0.915)^x\\), where \\(x\\) represents the distance from the speaker in meters and \\(\hat{y}\\) represents the predicted sound level in decibels. use the model to estimate the sound level at 10 meters away from the speaker. 62.7 decibels 38.63 decibels 25.79 decibels 9.15 decibels

Explanation:

Step1: Substitute x=10 into the model

$\hat{y} = 62.7(0.915)^{10}$

Step2: Calculate $(0.915)^{10}$

$(0.915)^{10} \approx 0.431$

Step3: Compute the product

$\hat{y} \approx 62.7 \times 0.431 \approx 25.79$

Answer:

25.79 decibels