Logarithms on Shaky GroundThe Richter scale was once the most commonscale used for measuring the magnitude of earthquakes. The Richter magnitude of an earthquake is given by the equation =−, where Iis the intensityof the earthquake measured by the amplitude of a seismograph reading taken 100 kilometers from the earthquake’s epicenter. The intensities of earthquakesvary greatly, from 0 in some cases to 800,000,000 or more in other cases, which is why a logarithmic scale is oftenused to measure their magnitudes. Part A) One of the strongest earthquakes ever recorded had a magnitude of 8.9 on the Richter Scale. What wasthe intensityof this earthquake? What would be the magnitude of an earthquake four times as weakasthis one?How many times as intensewas this earthquake as the magnitude 2 earthquake that struck central New Jersey in 2012?
Part B) Suppose a given earthquake is twice as intenseas another earthquake. Determine the difference in magnitude betweenthem.