# The Richter scale provides a measure of the magnitude of an earthquake. The following formula shows a relationship between the amount of energy

Question:The Richter scale provides a measure of the magnitude of an earthquake. The following formula shows a relationshipbetween the amount of energy released and the Richter number.2 EM ‘ 3 &quot;’9 0.00? where E is measured in kilowatt—hours. a. What value of E gives a Richter number M = 8.1? (Use scientiﬁc notation. Use the multiplication symbol in the math palette as needed. Round to three decimal places asneeded.) b. If a particular household uses 243 kWh per month, how many months would the energy released by an earthquake ofthis magnitude power 10 million households? (Round to one decimal place as needed.) c. Find the rate of change of the Richter number M with respect to energy when E = 80,000 kWh. (Round to seven decimal places as needed.) Why does one use the absolute value of x or of 90:) in the derivative formulas for the natural logarithm? Choose the correct answer below. 0 A. Since the derivative of — In (x) is the same as the derivative of In x (or the derivative of — In g(x) is the same as the derivative of In g(x)), an absolute value inside of a logarithm hasno effect on the derivative, other than making the result valid for more values of x. O B. Since the derivative of In ( — x) is the same as the derivative of — In x (or the derivative ofIn ( — g(x)) is the same as the derivative of — In 900), an absolute value inside of a logarithmhas no effect on the derivative, other than making the result valid for more values of x. O C. Since the derivative of In ( — x) is the same as the derivative of In x (or the derivative ofIn ( — g(x)) is the same as the derivative of In g(x)), an absolute value inside of a logarithm hasno effect on the derivative, other than making the result valid for more values of x.

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