what is the relationship between a one-point increase in magnitude and the amount of energy released by an earthquake?

10 times.

An earthquake with a magnitude of 5.0 is 10 times weaker than one with a magnitude of 6.0 and 100 times weaker than one with a magnitude of 7.0.

thank you =)

The relationship between a one-point increase in magnitude and the amount of energy released by an earthquake is not a straightforward linear relationship, but rather an exponential one. The magnitude of an earthquake is typically measured using the Richter scale or the Moment Magnitude Scale (Mw).

To understand this relationship, you need to know that the magnitude scale is logarithmic. The Richter scale is based on the amplitude of seismic waves recorded by seismometers, while the Moment Magnitude scale estimates the earthquake's total energy release based on the area of the fault that slipped, the average amount of slip, and the rigidity of the rocks involved.

Each whole number increase on the Richter scale represents a tenfold increase in the amplitude of seismic waves and approximately 31.6 times more energy released. For example, a magnitude 4 earthquake releases about 31.6 times more energy than a magnitude 3 earthquake, and a magnitude 5 earthquake releases about 1,000 times more energy than a magnitude 3 earthquake.

Therefore, a one-point increase in magnitude corresponds to a significant increase in the amount of energy released. It is important to note that the effects of an earthquake on the ground and human structures are also influenced by other factors, such as distance from the epicenter and local geology.