Question

The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula isR = log(I). The March 25, 2002 earthquake in Afghanistan measured 6.1 on the Richter scale. The Orange County earthquake in December 14, 2001 measured 3.9on the scaleHow many timesmore intense was the Afghanistan earthauake than the Orange County earthquake? Round youranswer to two decimal places.

Answer 1

Explanation

We are required to compare the intensities of the earthquake in Afghanistan and Orange country

To do so, we will follow the steps

Step 1: Find the intensity of the earthquake in Afghanistan

$\begin{gathered} R=log(I) \\ where \\ R=6.1 \\ \end{gathered}$$\begin{gathered} 6.1=logI \\ applying\text{ logarithm laws} \\ I=10^{6.1}=1258925.41 \end{gathered}$

Thus, the intensity of the earthquake in Afghanistan is 1258925.41

Step 2: Find the intensity of the Orange County earthquake

$\begin{gathered} R=log(I) \\ where \\ R=3.9 \\ 3.9=logI \\ If\text{ we make I the subject of the formula} \\ I=10^{3.9} \\ I=7943.28 \end{gathered}$

Therefore, the intensity of the Orange County earthquake is 7943.28

Step 3: Compare the intensity

$\frac{Intensity\text{ of Afghanistan earthquake}}{intensity\text{ of Orange County earthquake}}=\frac{1258925.41}{7943.28}$

$\frac{1,258,925.41}{7,943.28}=158.49$

Thus, the intensity of the earthquake in Afghanistan is 158.49 times more than the intensity of the earthquake in Orange County