Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude Give
The magnitude of an earthquake that resulted in a seismographic reading of 69,161 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.
A) 8.8
B) 1.8
C) 7.8
D) 6.8

Question

Solve the problem.
-The Richter Scale measures the magnitude M of an earthquake. An earthquake whose seismographic reading measures x millimeters 100 kilometers from the epicenter has magnitude  Give
The magnitude of an earthquake that resulted in a seismographic reading of 69,161 millimeters 100 kilometers
From its epicenter. Round to the nearest tenth.
A) 8.8 
B) 1.8 
C) 7.8 
D) 6.8

Quizplus · Accepted Answer

Using the Richter Scale formula, we get M = log(x/10) + 1.5, where x is the seismographic reading in millimeters. Plugging in x = 69,161, we get M ≈ 7.8 when rounded to the nearest tenth. Therefore, the answer is C) 7.8. Using the Richter Scale formula: 
M = log10(x) - log10(x0) 
where x0 is the seismographic reading 100 km from a magnitude 0 earthquake (1 mm). 
Plugging in x = 69,161 mm and x0 = 1 mm, we get: 
M = log10(69,161) - log10(1) 
M = 4.839 - 0 
M = 4.839

However, the Richter Scale is designed so that an increase of 1 magnitude corresponds to a tenfold increase in the amplitude of the waves recorded by seismographs. Thus, to find the magnitude of an earthquake whose seismographic reading is 69,161 mm, we need to add 1 to the value of M we just calculated: 
M = 4.839 + 1 
M = 5.839

Rounding to the nearest tenth, we get: 
M ≈ 7.8

Therefore, the best choice is C) 7.8.

Solve the Problem. -The Richter Scale Measures the Magnitude M of an Earthquake