This problem uses the Richter scale for the strength of an earthquake. The strength, $W$, of the seismic waves of an earthquake is compared to the strength, $W_{0}$, of the seismic waves of a standard earthquake. The Richter scale rating, $M$, is
\[
M=\log \left(\frac{W}{W_{0}}\right)
\]
In 2017 the Belair earthquake near Washington, DC, had a Richter-scale rating of 4.1. ${ }^{1}$ How many times more powerful were the seismic waves of the Belair earthquake than standard seismic waves?
Round your answer to the nearest integer.
The seismic waves of the Belair earthquake were
i
t times more powerful than standard seismic waves.

Step 1 ：The problem uses the Richter scale for the strength of an earthquake. The strength, \(W\), of the seismic waves of an earthquake is compared to the strength, \(W_{0}\), of the seismic waves of a standard earthquake. The Richter scale rating, \(M\), is \[M=\log \left(\frac{W}{W_{0}}\right)\]

Step 2 ：In 2017 the Belair earthquake near Washington, DC, had a Richter-scale rating of 4.1. The question is asking for the ratio of the strength of the seismic waves of the Belair earthquake to the strength of the seismic waves of a standard earthquake.

Step 3 ：This ratio can be found by rearranging the formula for the Richter scale rating to solve for \(W/W_{0}\): \[W/W_{0} = 10^M\]

Step 4 ：Given that the Richter scale rating of the Belair earthquake is 4.1, we can substitute this value into the formula to find the ratio. \[M = 4.1\]

Step 5 ：Calculate the ratio: \[W_{ratio} = 10^{M} = 12589.254117941662\]

Step 6 ：Round the ratio to the nearest integer: \[\text{round}(W_{ratio}) = 12589\]

Step 7 ：Final Answer: The seismic waves of the Belair earthquake were \(\boxed{12589}\) times more powerful than standard seismic waves.