Use the formula $L = 10 log_{10} (I/I_0)$, where $I_0 = 10^{-12} W/m^2$. Substitute the given intensity $I$ into the formula and calculate the value of $L$.

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.

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

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.

A function that is the inverse of an exponential function, used to model proportional growth or repeated multiplication.

A unit used to measure sound level, which has a logarithmic relationship with sound intensity.

The power of sound per unit area, typically measured in watts per square meter ($W/m^2$).

Reference intensity, the threshold of human hearing, approximately $10^{-12} W/m^2$.

A statistical method used to model the relationship between variables when one variable changes logarithmically with respect to the other.

A statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

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

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