486 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 65. Earthquake Intensity The magnitude of an earthquake, measured on the Richter scale, is log10 I I0 , where I is the amplitude registered on a seismograph 100 km from the epicenter of the earthquake, and I0 is the amplitude of an earthquake of a certain (small) size. Find the Richter scale ratings for earthquakes having the following amplitudes. (a) 1000I0 (b) 1,000,000I0 (c) 100,000,000I0 66. Earthquake Intensity On December 26, 2004, an earthquake struck in the Indian Ocean with a magnitude of 9.1 on the Richter scale. Express this reading in terms of I0 to the nearest hundred thousand. 67. Earthquake Intensity On February 27, 2010, an earthquake struck Chile with a magnitude of 8.8 on the Richter scale. Express this reading in terms of I0 to the nearest hundred thousand. 68. Earthquake Intensity Comparison Compare the answers to Exercises 66 and 67. How many times greater was the force of the 2004 earthquake than that of the 2010 earthquake? 69. (Modeling) Bachelor’s Degrees in Interdisciplinary Studies The table gives the number of bachelor’s degrees in interdisciplinary studies (in thousands) earned at U.S. colleges and universities from 2010–2016. Let x represent the number of years since 2009. Thus, x = 1 represents 2010, x = 2 represents 2011, and so on. Year Degrees Earned (in thousands) 2010 37.7 2011 42.5 2012 45.7 2013 47.7 2014 48.4 2015 47.6 2016 48.8 Data from National Center for Education Statistics. The following function is a logarithmic model for the data. ƒ1x2 = 38.5 + 5.74 ln x Use this function to estimate the number of bachelor’s degrees in interdisciplinary studies earned in the year 2020 to the nearest tenth of a thousand. What assumption must we make to estimate the number of degrees in years beyond 2016? 70. (Modeling) Value of Camper Shipments The table gives the forecasted value of camper shipments (in billions of dollars) in the United States from 2011 through 2020. The function ƒ1t2 = 8.10 + 3.01 ln t, t Ú 1, Year Camper Shipments (in billions of dollars) 2011 7.6 2012 10.3 2013 11.8 2014 12.4 2015 13.4 2016 14.0 2017 13.9 2018 13.8 2019 14.5 2020 14.8 Data from National Center for Education Statistics. where t represents the number of years since 2010 and ƒ1t2 is the value of camper shipments in billions of dollars, approximates the data reasonably well. Use the function to approximate the value of camper shipments in 2017 to the nearest billion. How does this approximation compare to the value given in the table?
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