a decibel is a logarithmic unit that can be used to measure the intensity of a sound. the function $y = 10\log x$ 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

Question

a decibel is a logarithmic unit that can be used to measure the intensity of a sound. the function $y = 10\log x$ 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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Logarithmic Functions" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Logarithmic Evaluation" ] } ## Identify the given function and variables Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &y = 10\log x\ &x = 100 \end{aligned} $$ ## Evaluate the logarithmic expression Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &y = 10\log(100)\ &\log(100) = 2\ &y = 10 \times 2 = 20 \end{aligned} $$ 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. 20 decibels { "elements": [ { "type": "functiongraph", "params": [ { "js": "10 * Math.log10(x)", "latex": "10\log_{10}(x)" }, 0.1, 150 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = 10log(x)", "withLabel": true } }, { "type": "point", "params": [ [100, 20] ], "properties": { "name": "(100, 20)", "size": 4, "color": "#F2557F", "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Functions" ] }

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Question

Explanation:

Identify the given function and variables

Evaluate the logarithmic expression

Answer: