to Logarithmic Functions Use this Word document to help organize your answers. 1. Record the location, date, and magnitude for the 5 largest earthquakes in the United States in the last 200 years in the table below. (Leave off Cascadia subduction zone because it occurred in 1700.) Then do the same for the largest earthquakes recorded in California, Hawaii, Washington, and North Carolina. (Yes, you read correctly!) Location Date Magnitude (y) 1 2 3 4 5 California Hawaii Washington North Carolina 2. The Richter scale was computed for each of these earthquakes using the forR , where R is the Richter magnitude and E is the energy of mula the quake. Convert this to an Exponential Equation. Show all steps. Remember you goal is to get E alone. 3. Use the Exponential Equation you found in Question 2 to find the Energy (E) of each earthquake. Record each energy in scientific notation rounded to 4 decimal places in the table. Location Energy (x) 1 2 3 4 5 California Hawaii Washington North Carolina 1. Make a scatter plot with these points in your graphing calculator. Use the energy on the horizontal axis (x) and the magnitude on the vertical axis (y). Include a screen shot of your scatterplot and viewing Window settings. 2. Describe which toolkit function the scatter plot resemble. 3. Find the logarithmic regression for the data. Round to 4 decimal places. Replace y and x with R and E. 4. The 1906 San Francisco earthquake was the second largest earthquake in California, as of March 18, 2013. Use the logarithmic regression to find the energy of the earthquake. Show all work and round to 4 decimal places. 5. Suppose there is an earthquake with an energy of 3.1939 x 10 12. According to your logarithmic regression, what is the Richter magnitude that will be reported on the news? Show the equation used, value substituted, and final answer rounded to the nearest tenth. Self Check Recall the formula was used in Question 2 to find the Richter magnitude, R. Use this formula to find the magnitude of an earthquake with an intensity (E) of 3.1939 x 1012. Compare this to your result in Question 8 to check your answer. They should be the same. R