Question 20 (5 points) The Richter Scale gives a mathematical model for the magn

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Question 20 (5 points) The Richter Scale gives a mathematical model for the magnitude of an earthquake in terms of the ratio of the amplitude earthquake wave (also known as the intensity of an earthquake) to the amplitude of the smallest detectable wave (also known as the amplitude of the earthquake wave) of the earthquake by A, and the amplitude of the smallest detectable wave by S, then we can model these values by the formula R=log ( S |- In 1906, San Francisco felt the impact of an earthquake with a magnitude of 7.8. Many pundits claim that the worst is yet to come, with an earthquake 401,950 times as intense as the 1989 earthquake ready to hit San Francisco. If the pundits ability to predict such earthquakes were correct, what would be the magnitude of their claimed earthquake? Round your answer to the nearest tenth. Your Answer: Answer

Explanation / Answer

Given the earthquake model equation

R = log (A/S), with the quantities R,A and S having meaning as stated.

Now, present earthquake in San Francisco has magnitude, R = 7.8, so, 7.8 = log (A/S)

According to pundits, the future earth quake will have intensity, A' = 401950 × A

Hence, future earthquake will have magnitude

R' = log (A'/S) = log (401950 × A/S)

= log (401950) + log (A/S)

= log (401950) + 7.8

= 5.60417 + 7.8 = 13.40417

Therefore, required magnitude = 13.4

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