Final answer:
To find the energy released by an earthquake with a magnitude of 6.0, one must rearrange and solve the function R = 0.67 log(0.37E) + 1.46 for E, the energy released in kilowatt-hours. Through a series of algebraic steps, including logarithmic manipulation, the approximate energy can be determined.
Step-by-step explanation:
The student's question pertains to the calculation of the energy released by an earthquake when its magnitude is known. Given the function R = 0.67 log(0.37E) + 1.46, and an earthquake magnitude R of 6.0, we need to solve for E, the energy in kilowatt-hours. Solving the equation R = 0.67 log(0.37E) + 1.46 for E when R = 6.0 involves the following steps:
- Subtract 1.46 from both sides of the equation: 6.0 - 1.46 = 0.67 log(0.37E).
- Divide both sides by 0.67: (6.0 - 1.46)/0.67 = log(0.37E).
- Compute the left side to get the logarithm value.
- Use the property of logarithms to solve for E: 10^(logarithm value) = 0.37E.
- Divide both sides by 0.37 to find the approximate energy E released.
To provide the approximate energy released by this earthquake, you would calculate the expressions above to find E. Keep in mind that the Richter scale is logarithmic, so each whole number increment represents a tenfold increase in the measured amplitude of the earthquake waves and correspondingly, roughly 31.6 times more energy release.