Chapter 4.6, Problem 38E

To determine

Calculate how many times more intense was the earthquake.

Answer to Problem 38E

  $\boxed{2.5}$

Explanation of Solution

Given information:

The Northridge, California, earthquake of $1994$ had a magnitude of $6.8$ on the Richter scale. A year later, a $7.2$ -magnitude earthquake struck Kobe, Japan. How many times more intense was the Kobe earthquake than the Northridge earthquake?

Calculation:

Consider the intensity $I_1$ and $I_2$ for $1994$ and $1995$ earthquake.

  $\begin{array}{l}\log \frac{I_1}{I_2}=\log \frac{I_1}{S}-\log \frac{I_2}{S}\\ \log \frac{I_1}{I_2}=7.2-6.8\\ =0.4\\ so,\\ \frac{I_1}{I_2}={10}^{\log \frac{I_1}{I_2}}\\ ={10}^{0.4}\\ =2.5118\\ \approx 2.5\end{array}$

So, the intensity of $1995$ earthquake is $\boxed{2.5}$ times more than $1994$ earthquake.

Hence, the solution is, $\boxed{2.5}$