Activity 7.1, Richter Scale and Logarithms

0. Work Exploration #6, in Topic 7, on page 131 in the textbook, and hand it in on a separate piece of paper.

In this activity, you will investigate earthquake data and explore the Richter scale as a measure of the intensity of an earthquake. You will consider how numbers on this scale compare with one another and study logarithms in the process.

1. Simply retrieve the file EA7.1.1 Deadly Earthquakes.xls. (These data were obtained from the website http://earthquake.usgs.gov.) This file contains the date, location, and magnitude on the Richter scale of earthquakes that occurred from 1975–2008 and involved the loss of 1,000 or more lives.

2. Sort the data in ascending order by magnitude and give the date and location of the strongest and weakest of the earthquakes on the list. (See Activity 1.2 if you do not remember how to sort data.) You do not need to paste the sorted data into your MS Word document, you should just be sure to enter the strongest and the weakest.

3. How many times stronger was the strongest earthquake than the weakest?

4. For each of the earthquakes listed, compute the relative energy it released using the following instructions. Recall that the relative energy E released by an earthquake of magnitude m on the Richter scale is E = 10^m. Once you have performed the necessary calculations, you should paste all the data into your MS Word document.

6. Create a scatterplot using columns C and D of your spreadsheet. (See Activity 2.1 if you do not remember how to create a scatterplot. Be sure to label your axes.) Copy and paste this scatterplot into your MS Word document.

6. a. Explain what your graph shows.

6. b. What type of function (linear, exponential, or neither linear nor exponential) does your graph show? How do you know?

6. c. What variable is on the horizontal axis? What variable is on the vertical axis?

7. For each energy value E you found, compute its logarithm log E, using the following instructions. You do NOT need to paste this updated table into your MS Word document.

8. How are the values you just calculated in column E related to other values in your table?

9. Create another scatterplot using columns D and E, and copy and paste this scatterplot into your MS Word document. What variable is on the horizontal axis? What variable is on the vertical axis?

10. Look at the two scatterplots you’ve created in this activity and describe how they are related. How could you obtain one from the other?

11. Retrieve the file EA7.1.2 Earthquake Casualt.xls. This file gives the same information as the file you used previously, except a new column has been added that shows estimated number of deaths. Create a scatterplot to show if there is any relationship between magnitude and number of deaths. Copy and paste this scatterplot into your MS Word document.

Explain in detail what your graph shows. (You might want to delete one or two “unusual data values” to see what the data shows. Be sure to explain what you did.)

Summary
In this activity, you compared strengths of major earthquakes from 1975 to 2008. You explored the relationship between the earthquake’s magnitude on the Richter scale and the relative energy released in the earthquake. You used Excel to draw graphs of the logarithmic and exponential functions involved and analyzed how they are related. You also used Excel to compute values of the common logarithmic function and to write numbers in scientific notation.