Activity 7.1

Richter Scale and Logarithms

10 points

Due at the beginning of class, Wednesday, March 4, 2009

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. How much stronger is an earthquake that measures 6.5 on the Richter scale than one that measures 6.0?  (Think about the formulas we discussed in class!)

Next, how much farther away from your home is a restaurant that is 6.5 blocks away, as compared to one that is 6.0 blocks away?

How are these measures similar and how are they different?

2. Simply retrieve the fille 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 to 2008 and involved the loss of 1,000 or more lives.

3. 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 should not paste the sorted data into your Word document, but you should include the strongest and the weakest.

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

5. 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 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 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?

6. d. 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 should NOT paste this updated table into your 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 Word document.

9. a. Give the name and equation of the function just graphed.

9. b. What variable is on the horizontal axis?

9. c. 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. Here are instructions to use Excel to write in scientific notation the relative energy released by the first earthquake on the list. You should NOT paste this updated table into your Word document.

12. Write the number as it appears in cell F2 and also write it in standard scientific notation (using a power of 10).

13. What is the difference between the number in cell D2 and the number in cell F2?

14. Using the “drag” feature, enter the rest of the numbers in column D into column F in scientific notation (but do NOT paste this into your Word document). Estimate the ratio between the largest number and the smallest number in column F. What does this ratio say about the earthquakes given in the data set?

15. 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 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 earthquakes' magnitude on the Richter scale and the relative energy released in the earthquakes. 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.