521 Solve each problem. 70. (Modeling) Decibel Levels Decibel rating of the loudness of a sound is modeled by the formula d = 10 log I I0 , where I is the intensity of a particular sound, and I0 is the intensity of a very faint threshold sound. A few years ago, there was a controversy about a proposed government limit on factory noise. One group wanted a maximum of 89 decibels, while another group wanted 86. Find the percent by which the 89-decibel intensity exceeds that for 86 decibels. 71. Earthquake Intensity The magnitude of an earthquake, measured on the Richter scale, is log 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. On November 30, 2018, Anchorage, Alaska was shaken by an earthquake that measured 7.0 on the Richter scale. (a) Express this reading in terms of I0. (b) On August 18, 2018, a quake measuring 8.2 on the Richter scale struck off the coast of Fiji. It was the largest earthquake in 2018. Express the magnitude of an 8.2 reading in terms of I0 to the nearest hundred thousand. (c) How much greater than the force of the 7.0 earthquake was the force of the earthquake that measured 8.2? 72. Earthquake Intensity The San Francisco earthquake of 1906 had a Richter scale rating of 8.3. (a) Express the magnitude of this earthquake in terms of I0 to the nearest hundred thousand. (b) In 1989, the San Francisco region experienced an earthquake with a Richter scale rating of 7.1. Express the magnitude of this earthquake in terms of I0 to the nearest hundred thousand. (c) Compare the magnitudes of the two San Francisco earthquakes discussed in parts (a) and (b). 73. Interest Rate What annual interest rate, to the nearest tenth, will produce $4700 if $3500 is left at interest compounded annually for 10 yr? 74. Growth of an Account Find the number of years (to the nearest hundredth) needed for $48,000 to increase to $53,647 at 2.8% interest compounded (a) semiannually and (b) continuously. 75. Growth of an Account Manuel deposits $10,000 for 12 yr in an account paying 3% interest compounded annually. He then puts this total amount on deposit in another account paying 4% interest compounded semiannually for another 9 yr. Find the total amount on deposit after the entire 21-yr period. 76. Growth of an Account Anne deposits $12,000 for 8 yr in an account paying 2.5% interest compounded annually. She then leaves the money alone with no further deposits at 3% interest compounded annually for an additional 6 yr. Find the total amount on deposit after the entire 14-yr period. 77. Cost from Inflation Suppose the inflation rate is 4%. Use the formula for continuous compounding to find the number of years, to the nearest tenth, for a $1 item to cost $2. CHAPTER 4 Review Exercises
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