By what factor does the intensity increase for each whole-number increase in the Richter scale? Use your understanding of logarithms and the inverse relationship between logarithms and exponents to explain your answer.

Answer:

The intensity of an earthquake increases by a factor of 10 for each whole-number increase on the Richter scale. This is because the Richter scale is based on common logarithms (base 10). According to the inverse relationship between logarithms and exponents, an increase of 1 in magnitude corresponds to an intensity increase of 10^1. For example, a magnitude 3 earthquake is 10^3 times more intense than a standard earthquake, while a magnitude 2 earthquake is 10^2 times more intense; since 10^3 = 10^2 × 10, the intensity is 10 times greater.