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

Explanation:

Step1: Recall the 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 Chile 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 the 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 $\frac{10^{9.5}}{10^{7.0}}=10^{9.5 - 7.0}=10^{2.5}$.

Step4: Calculate the value of $10^{2.5}$

$10^{2.5}=10^{2+\ 0.5}=10^{2}\times10^{0.5}=100\times\sqrt{10}\approx100\times3.16 = 316$.

Answer:

D. 316