Final answer:
To calculate the intensity of an earthquake that registered 7.4 on the Richter scale with a reference intensity of 2.0 × 1011, use the formula I = I0 × 10M, resulting in an intensity of 5.01187 × 1018.
Step-by-step explanation:
The Richter scale is a logarithmic scale used to represent the intensity of an earthquake. Given that the earthquake registered 7.4 on the Richter scale and the reference intensity is 2.0 × 1011, we can calculate the actual intensity of the quake. The formula to convert from Richter scale (M) to intensity (I) is given by:
I = I0 × 10M - M0
Where I0 is the reference intensity, and M0 is the magnitude at which the reference intensity is defined. If we are comparing to an earthquake of magnitude 0, M0 will be 0. Thus, for the earthquake of magnitude 7.4, its intensity (I) can be calculated as follows:
I = 2.0 × 1011 × 107.4
After performing the calculations:
I = 2.0 × 1011 × 107.4 = 5.01187 × 1018
This is the calculated intensity of the earthquake that registered 7.4 on the Richter scale.