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The magnitude M of an earthquake on the Richter scale is defined as a function of the energy, in joules, E released by the earthquake:
Using this equation, it can be shown that
Find the values of a and b.
On July 22, 2023, Taylor Swift fans in Seattle registered a 2.3 magnitude earthquake. The largest earthquake ever recorded, the 1960 Valdivia earthquake off the coast of Chile, had a 9.5 magnitude.
Find the number of "Swift Quakes" needed to match the energy of the Valdivia earthquake. Give your answer in the form c×10k, where 1≤c<10 and k∈Z.
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