The Richter scale reading for an earthquake measures its intensity (as a multiple of some minimum intensity used for comparison). The intensity I corresponding to a Richter scale reading R is given by. An earthquake occurred near San Francisco in 1923 that measured 7.3; another earthquake occurred in 1947 that measured 8.5. Calculate the ratio of these intensities (larger to smaller). Round your answer to six decimal places.
A) 0.063096
B) 1.164384
C) 14.601032
D) 15.848932
E) 0.010135

Question

The Richter scale reading for an earthquake measures its intensity (as a multiple of some minimum intensity used for comparison). The intensity I corresponding to a Richter scale reading R is given by. An earthquake occurred near San Francisco in 1923 that measured 7.3; another earthquake occurred in 1947 that measured 8.5. Calculate the ratio of these intensities (larger to smaller). Round your answer to six decimal places. 
A) 0.063096 
B) 1.164384 
C) 14.601032 
D) 15.848932 
E) 0.010135

Quizplus · Accepted Answer

The intensity ratio is given by:

$I=\frac{10^{11/2R}}{10^{11/2R'}}=\left(\frac{10^{11/2}}{10^{11/2}}\right)^{R-R'}$

Substituting R=8.5 and R'=7.3, we get:

$I=\left(\frac{10^{11/2}}{10^{11/2}}\right)^{8.5-7.3}=10^{11/2(8.5-7.3)}=10^{0.475}=15.848932$

Therefore, the ratio of intensities is 15.848932, which is closest to answer choice D.

The Richter Scale Reading for an Earthquake Measures Its Intensity