Question

a decibel is a logarithmic unit that can be used to measure the intensity of a sound. the function y = 10logx gives the intensity of a sound in decibels, where x is the ratio of the intensity of the sound to a reference intensity. the reference intensity is generally set at the threshold of hearing. use the graphing utility to graph the decibel function. the sound intensity of rustling leaves is 100 times the reference intensity. use your graph to determine the sound intensity of rustling leaves in decibels. decibels done

Explanation:

Step1: Identify the value of x

The ratio \( x \) is given as 100 (since the sound intensity of rustling leaves is 100 times the reference intensity).

Step2: Substitute x into the decibel function

We use the function \( y = 10\log x \). Substitute \( x = 100 \) into the function:
\[
y = 10\log(100)
\]

Step3: Evaluate the logarithm

We know that \( \log(100)=\log(10^2) = 2 \) (since \( \log(a^b)=b\log(a) \) and \( \log(10) = 1 \)).

Step4: Calculate y

Substitute \( \log(100)=2 \) into the equation:
\[
y = 10\times2 = 20
\]

Answer:

20