Earthquake Magnitude and Richter Scale

What is the value of x when the Richter scale rating is 6.6?

Round your answer to the nearest hundredth.

a) x=10^−6.6

b) x=10^6.6

c) x=6.6^10

d) x=6.6^−10

Final answer:

For a Richter scale rating of 6.6, the correct expression to determine the value of x is x = 10^6.6, since the Richter scale is logarithmic using base 10.

The Richter scale is a logarithmic scale used to quantify the energy produced by an earthquake. A value of 6.6 on the Richter scale indicates a major earthquake. In terms of mathematics, when asked to find the value of x when the Richter scale rating is 6.6, we are dealing with powers of ten. This is because the Richter scale is based on a log base 10 scale.

Looking at the options provided, the correct expression to calculate x is x = 10^6.6, which corresponds to the amount of energy released by the earthquake. Hence, if we round our answer to the nearest hundredth, the value of x would still be x = 10^6.6 as this is already in its simplest form and rounding does not apply to the exponent directly.

The answer is therefore (b) x = 10^6.6.