<p> Logarithms and the Richter Scale Project Overview</p><p>This problem-solving RWLO is intended for use in an Intermediate Algebra course. The focus is based on the application of logarithms as used in the Richter Scale, which identifies the magnitude of earthquakes. In addition, the relationship between basic exponential and logarithmic functions is emphasized.</p><p>The Logarithms and the Richter Scale RWLO requires students to identify the Richter Scale values of earthquakes using an internet site. Students will write the equivalent of each Richter Scale value in logarithmic form as a basic logarithmic equation. Then, students will write each logarithmic equation as an exponential equation. Students will write a ratio of exponential expressions, which evolve from the exponential equations and then, express or compare the intensities of earthquakes. </p><p>1 Student Learning Objectives</p><p>For this RWLO, the student will be able to:</p><p> Identify the Richter Scale values of earthquakes using an internet site.  Given the definition of a Richter Scale value, write the equivalent of each Richter Scale value in logarithmic form as a basic logarithmic equation.  Write each logarithmic equation as an exponential equation.  Write a ratio of exponential expressions, which evolve from the exponential equations, of the greatest earthquake to the lesser earthquake.  Write a statement that identifies how many times more intense the earthquake with the greatest Richter Scale value is than the earthquake with the lesser Richter Scale value. </p><p>2 Procedure</p><p>Time: Approximately 30 minutes</p><p>Materials: Computer linked to the internet, pencil, paper, and scientific calculator</p><p>Implementation: This RWLO can be used either in the classroom or as an out of class assignment.</p><p>Steps:</p><p>1. Review writing a basic common (base 10) logarithmic equation as an exponential equation with students. 2. Explain that the basic definition of a Richter Scale value is:  I   c  log   R , where R is the Richter Scale value, I c is the intensity of the  I n </p><p>“movement” of the earth from the earthquake, and I n is the intensity of “movement” on a normal day to day basis. 3. Edit or customize the Earthquakes Worksheet (in the Assessment section) based on your locale. 4. Print a copy of the worksheet or edited version. Students will also need to print a copy of this worksheet or you may provide them with one (especially if you have customized it to your locale). 5. Access the appropriate websites as a class or as individual students. 6. Gather the necessary data or students will gather the data if working as individuals. 7. Students will complete the Earthquakes Worksheet. 8. After students complete the worksheets, collect them and evaluate. Then, return to the students and discuss. Or, discuss first, then collect the worksheets.</p><p>3 Content Material</p><p>Student Directions:</p><p>1. Obtain a copy of the Earthquake Worksheet, which is to be completed through the instructions that follow.</p><p>2. Identify the earthquake with the greatest Richter Scale value at http://www.iris.edu/seismon/last30days.phtml</p><p>3. Identify the earthquake with the greatest Richter Scale value in the student’s State within the United States or within the student’s country using http://earthquake.usgs.gov/</p><p> a. At the site, for US information select “Last EQ in Each State” and then select the appropriate state.</p><p> b. At the site, for other countries select “Last EQ in Each Country or Region”, and then select the appropriate country or region.</p><p> c. For direct link to the State of Ohio, www.dnr.state.oh.us/OhioSeis/html/eqcat01a.htm which is the first of 4 charts based on the time intervals of 1776 – 1899, 1900 – 1949, 1950 – 1999, 2000 – present. </p><p>4. Write the equivalent of each Richter Scale value in logarithmic form as a basic logarithmic equation.</p><p>5. Write each logarithmic equation as an exponential equation.</p><p>6. Write a ratio of exponential expressions, which evolves from the exponential equations and then, compare the intensities of earthquakes. </p><p>7. Write a statement that identifies how many times more intense the earthquake with the greatest Richter Scale value is than the Earthquake with the lesser Richter Scale value. </p><p>4 Referenced URLs:  http://www.iris.edu/seismon/last30days.phtml</p><p> http://earthquake.usgs.gov/</p><p> www.dnr.state.oh.us/OhioSeis/html/eqcat01a.htm</p><p>5 Assessment</p><p>The following is the recommended form of assessment: Earthquakes Worksheet Name ______(Each response is worth 2 points for a total of 30 points.)</p><p>A world-wide measure of the intensity of earthquakes is described by the Richter Scale. The basic definition of a Richter Scale value is:  I   c  log   R , where R is the Richter Scale value, I c is the intensity of the  I n </p><p>“movement” of the earth from the earthquake, and I n is the intensity of “movement” on a normal day-to-day basis.</p><p>1. The greatest recorded Richter Scale value for an earthquake is ______.</p><p> a. It occurred in (geographic location) ______.</p><p> b. The date of the earthquake was ______.</p><p> c. Using the logarithmic definition of a Richter Scale value, write the basic logarithmic equation for this Richter Scale reading. It is </p><p>______. </p><p> d. Write the basic logarithmic equation as a basic exponential equation. It is</p><p>______.</p><p>2. The greatest Richter Scale value for an earthquake in my locale is ______.</p><p> a. It occurred in (geographic location) ______.</p><p> b. The date of the earthquake was ______.</p><p> c. Using the logarithmic definition of a Richter Scale value, write the basic logarithmic equation for this Richter Scale reading. It is </p><p>______.</p><p>6 d. Write the basic logarithmic equation as a basic exponential equation. It is</p><p>______.</p><p>3. Of the two Richter Scale values, the greatest is ______.</p><p>4. Write a ratio, using the exponential forms of the greatest earthquake to the lesser earthquake. It is</p><p>______.</p><p>5. Reduce the ratio using the rules of exponents. It is </p><p>______.</p><p>6. Use scientific calculator to determine the value obtained in the previous step (step 5). It is </p><p>______.</p><p>7. Write a statement that identifies how many times more intense the earthquake with the greatest Richter Scale value is than the Earthquake with the lesser Richter Scale value. It is</p><p>______</p><p>______.</p><p>7 Links to Course Competencies</p><p>This RWLO could be applied in the following courses: Intermediate Algebra. Specifically, this RWLO meets the following course competencies:</p><p> Write basic logarithmic equations.</p><p> Write basic logarithmic equations in their equivalent form. </p><p> Analyze applications involving logarithms and exponential expressions or equations.</p><p> Apply the use of technology (calculators, computers, or internet).</p><p>8 Supplementary Resources</p><p> www.ohiodnr.com/OhioSeis/html/scales.htm</p><p> http:quake.wr.usgs.gov/</p><p> www.iris.edu/quakes/quakes.htm</p><p> For further on-line questions or research on earthquake access Ask.com</p><p>9 Recommendations</p><p>Recommendations for Integration and Extension: </p><p>This RWLO is intended for use in an Intermediate Algebra course to demonstrate the use of exponential and logarithmic functions in a realistic world application. It may be used as presented or extended. Examples for extension are:</p><p>1. Under what conditions would the ratio obtained in question 5 of the Earthquake Worksheet equal one? </p><p>2. Include a comparison of earthquakes that involves identifying an earthquake and its’ Richter Scale value closest to each students’ birthday. </p><p>3. Research the connection of the magnitude of seismic waves measured by the Richter Scale to the energy radiated by an earthquake, which is referred to as the “factor of 30”. Determine the corresponding energy radiated by the earthquakes identified by students in this RWLO.</p><p>Implementation:</p><p>This RWLO is designed for students to work individually or cooperatively in groups. Group size and designation are to be determined by the classroom instructor. If working in groups, students are to complete the Earthquake Worksheet independently. Allow approximately 5 minutes for explanation of the activity.</p><p>Prior to the class session, for each student, print out all the required materials referenced in the content material section of this RWLO and the Earthquake Worksheet.</p><p>Back-up: </p><p>A day or two prior to planned use of this RWLO, print a copy of information from each of the data files at the identified websites as a back-up for website inaccessibility.</p><p>10</p>