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  1. AP Pre Calculus
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How do you calculate the sound level in decibels given the sound intensity?

Use the formula L=10log10(I/I0)L = 10 log_{10} (I/I_0)L=10log10​(I/I0​), where I0=10−12W/m2I_0 = 10^{-12} W/m^2I0​=10−12W/m2. Substitute the given intensity III into the formula and calculate the value of LLL.

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How do you calculate the sound level in decibels given the sound intensity?

Use the formula L=10log10(I/I0)L = 10 log_{10} (I/I_0)L=10log10​(I/I0​), where I0=10−12W/m2I_0 = 10^{-12} W/m^2I0​=10−12W/m2. Substitute the given intensity III into the formula and calculate the value of LLL.

How do you create a logarithmic function model from a data set?

Use logarithmic regression on a calculator or software to find the logarithmic function that best fits the data. Identify the parameters of the model, such as the coefficients and constants.

How do you predict the sound level at an intensity of 0.0001 W/m2W/m^2W/m2 using the model y=10log10(x)y = 10 log_{10}(x)y=10log10​(x)?

Substitute x=0.0001x = 0.0001x=0.0001 into the model: y=10log10(0.0001)y = 10 log_{10}(0.0001)y=10log10​(0.0001). Calculate the value of yyy, which represents the predicted sound level in decibels.

How do you determine if a situation is best modeled by a logarithmic function?

Look for situations where changes in one variable result in proportional changes in another, especially when dealing with large ranges of values. Check if the data exhibits a logarithmic relationship.

What does the graph of a logarithmic function y=logb(x)y = log_b(x)y=logb​(x) tell us about its derivative?

The derivative of a logarithmic function represents the rate of change of the function. The graph shows that the rate of change decreases as xxx increases.

How does the graph of y=ln(x)y = ln(x)y=ln(x) compare to the graph of y=exy = e^xy=ex?

The graph of y=ln(x)y = ln(x)y=ln(x) is the reflection of the graph of y=exy = e^xy=ex over the line y=xy = xy=x, as they are inverse functions.

What is the formula for sound level in decibels (dB)?

L=10log10(I/I0)L = 10 log_{10} (I/I_0)L=10log10​(I/I0​) where LLL is the sound level, III is the sound intensity, and I0I_0I0​ is the reference intensity.

What is the general form of a logarithmic function?

y=mlogb(x)+cy = m log_b(x) + cy=mlogb​(x)+c, where yyy is the dependent variable, xxx is the independent variable, bbb is the base of the logarithm, and mmm and ccc are constants.

How to calculate the sound level at the stage?

L=10log10(1.0/10−12)=120extdBL = 10 log_{10} (1.0/10^{-12}) = 120 ext{ dB}L=10log10​(1.0/10−12)=120extdB

How to calculate the sound level in the front row?

L=10log10(0.1/10−12)=110extdBL = 10 log_{10} (0.1/10^{-12}) = 110 ext{ dB}L=10log10​(0.1/10−12)=110extdB

How to calculate the sound level in the middle of the crowd?

L=10log10(0.01/10−12)=100extdBL = 10 log_{10} (0.01/10^{-12}) = 100 ext{ dB}L=10log10​(0.01/10−12)=100extdB

How to calculate the sound level at the back of the crowd?

L=10log10(0.001/10−12)=90extdBL = 10 log_{10} (0.001/10^{-12}) = 90 ext{ dB}L=10log10​(0.001/10−12)=90extdB