In 2010, Haiti was hit by a devastating earthquake which registered at 7.0 on the Richter scale. The largest recorded earthquake since 1990 occurred in 1960 in valdivia chile and registered at 9.5 on the Richter scale. About how many times greater was the intensity of the Chilean earthquake?
Accepted Solution
A:
Answer: Approx 316.228 timesStep-by-step explanation:Let [tex]I_1[/tex] be the intensity of the earthquake in ChileAnd, [tex]I_2[/tex] be the intensity of the earthquake in Haiti,Since, Haiti was hit by a earthquake which registered at 7.0 on the Richter scale and Chile was hit by a earthquake which registered at 9.5 on the Richter scale,Thus, for Chile,[tex]9.5 = log (\frac{I_1}{I_0} )[/tex] --------(1) [ by the formula, [tex]R = log (\frac{I}{I_0} )[/tex] ]And, For Haiti,[tex]7 = log (\frac{I_2}{I_0} )[/tex] ----------(2),Equation (1) - Equation (1),[tex]2.5 = log (\frac{I_1}{I_0} )-log (\frac{I_2}{I_0} )[/tex]⇒ [tex]2.5 = log(\frac{I_1}{I_2} )[/tex]⇒ [tex]10^{2.5} = \frac{I_1}{I_2}[/tex]⇒ [tex]10^{2.5} = \frac{I_1}{I_2}[/tex]⇒ [tex]316.227766017 I_2=I_1[/tex]That is, the Intensity of Chile is approx 316.228 times of intensity of Haiti.