Frequency of earthquakes: The table below gives the average number N of earthquakes24 of magnitude at least M that occur each year worldwide. a. Gutenberg and Richter fitted these data with an...

Frequency of earthquakes: The table below gives the average number N of earthquakes24 of magnitude at least M that occur each year worldwide.

a. Gutenberg and Richter fitted these data with an exponential function. Find an approximate exponential model for the data.

b. How many earthquakes per year of magnitude at least 5.5 can be expected?

c. Gutenberg and Richter found that the model fit observed data well up to a magnitude of about 8, but for magnitudes above 8 there were considerably fewer quakes than predicted by the model. How many quakes per year of magnitude 8.5 or greater does the model predict?

d. What is the limiting value for N? Explain in practical terms what this means.

e. How does the number of earthquakes per year of magnitude M or greater compare with the number of earthquakes of magnitude M + 1 or greater?