Richter Scale and Logarithms

Transcription

1 activity 7.1 Richter Scale and Logarithms 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? 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. Retrieve the file EA7.1.1 Deadly Earthquakes.xls from the CD or website. (These data were obtained from the website This file contains the date, location, and magnitude on the

2 460 Excel Activities Richter scale of earthquakes that occurred from 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 dat) Strongest: 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. Instructions to Use Excel to Calculate Energy Released In cell D2, enter =10^C2 (the ^ symbol indicates raised to a power) to calculate the relative energy of the first earthquake. Enter an appropriate title in cell D1. To calculate the relative energy as a function of Richter scale magnitude for all earthquakes, use the drag feature of Excel to fill the column.

3 Activity 7.1: Richter Scale and Logarithms 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.) Explain what your graph shows. What type of function (linear, exponential, or neither linear nor exponential) does your graph show? How do you know? c. What variable is on the horizontal axis? 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. Instructions to Use Excel to Calculate Logarithms To have Excel compute these logarithms and enter them in column E, place the cursor in cell E2 and enter =LOG(D2). Then drag down. Enter an appropriate title for column E in cell E1.

4 462 Excel Activities 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. Give the name and equation of the function just graphed. What variable is on the horizontal axis? 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.

5 Activity 7.1: Richter Scale and Logarithms 463 Instructions to Use Excel to Write Scientific Notation c. In cell F2, enter =D2 to copy the number in cell D2 (which represents the relative energy released by the earthquake) into cell F2. Click on cell F2, go to the Cells group and select Format. Click on Format Cells. In the Format cells window, click the Number tab and choose Scientific from the Category list. For Decimal places, enter 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. 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?

6 464 Excel Activities 15. Retrieve the file EA Earthquake Casualt.xls from the CD or website. 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. 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 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.