in 2010 haiti was hit by a devastating earthquake, which registered at 7.0 on the richter scale. the largest…

Explanation:

Step1: Recall Richter - scale formula

The Richter - scale formula is $M=\log\left(\frac{I}{I_0}\right)$, where $M$ is the magnitude, $I$ is the intensity of the earthquake, and $I_0$ is a reference intensity. For the Haiti earthquake with magnitude $M_1 = 7.0$, we have $7.0=\log\left(\frac{I_1}{I_0}\right)$, so $\frac{I_1}{I_0}=10^{7.0}$. For the Chilean earthquake with magnitude $M_2 = 9.5$, we have $9.5=\log\left(\frac{I_2}{I_0}\right)$, so $\frac{I_2}{I_0}=10^{9.5}$.

Step2: Find the ratio of intensities

We want to find $\frac{I_2}{I_1}$. Since $\frac{I_1}{I_0}=10^{7.0}$ and $\frac{I_2}{I_0}=10^{9.5}$, then $\frac{I_2}{I_1}=\frac{\frac{I_2}{I_0}}{\frac{I_1}{I_0}}=\frac{10^{9.5}}{10^{7.0}}$.

Step3: Use the exponent rule

According to the exponent rule $\frac{a^m}{a^n}=a^{m - n}$, so $\frac{10^{9.5}}{10^{7.0}}=10^{9.5 - 7.0}=10^{2.5}$. And $10^{2.5}\approx316$.

Answer:

316