The Exponential and Logarithmic Functions Source Larson upse

The Exponential and Logarithmic Functions (Source: Larson, upseis, Northridge) & of Earthquake strain that has accumulated Earthquakes, the sudden movement the earth caused by release of years. It is therefore of of almost everyone in recent the two over a period oftime, captivated the attention and educators be introduced of for educational purposes that both students Magnitude refers to the measurement fundamental concepts of intensity and the severity of energy released when a fault ruptures, while intensity is a number that and their and on humans in terms of its effects on the The Richter Scale is commonly used to measure the magnitude of an An of scale. means that an increase of one in magnitude the Richter magnitude is the amplitude of ground motion. to a factor of ten increase in (I) is given by, (R) oran earthquake of intensity On the Richter Scale, the m In (10) where Io is the minimum intensity used for comparison. Assume Io 1. Questions: (Part earthquake which had a magnitude of 8.3 1. Find the intensity of the 1906 San Francisco (R 8.30 on the Richter scale. 2. Find the intensity of the 2011 Japan earthquake which had a magnitude of9.0 (R 9.0) on the Richter Scale.

Solution

1) R = [lnI - lnIo]/ln10

Io = 1; R = 8.3

8.3*ln10 = lnI - 0

lnI = ln(10^8.3)

I = 10^8.3 = 199526231.496

2) R = 9.0 Io = 1; find I

R = [lnI - lnIo]/ln10

9*ln10 = lnI - 0

lnI = ln10^9

I = 1000000000