Updated for Excel 2007
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 http://earthquake.usgs
.gov/.) This file contains the date, location, and magnitude on the
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Richter scale of earthquakes that occurred from 1975–2003 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.)
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 = 10m.
Instructions to Use Excel to Calculate
Energy Released
a.
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.
b.
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.
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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.)
a.
Explain what your graph shows.
b.
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
a.
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.
b.
Enter an appropriate title for column E in cell E1.
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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.
a.
Give the name and equation of the function just graphed.
b.
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.
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Instructions to Use Excel to Write
Scientific Notation
a.
In cell F2, enter =D2 to copy the number in cell D2 (which represents the
relative energy released by the earthquake) into cell F2.
b.
Click on cell F2, go to the Cells group and select Format. Click on Format
Cells.
c.
In the Format cells window, click the Number tab and choose Scientific
from the Category list. For Decimal places, enter 2.
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. 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?
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Excel Activities
15. Retrieve the file “EA.7.1.2 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 2003.
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.