499 4.5 Exponential and Logarithmic Equations 107. Average Annual Public University Costs The table shows the cost of a year’s tuition, room and board, and fees at 4-year public colleges for selected years from 1970 through 2016. Letting y represent the cost in dollars and x the number of years since 1970, the function ƒ1x2 = 142711.062x models the data quite well. (a) Use the function to estimate the average annual cost, to the nearest dollar, of a year’s tuition, room and board, and fees in 2018. (b) If this trend continues, approximately when will the average annual cost of a year’s tuition, room and board, and fees reach $25,000? Year Average Annual Cost 1970 $1326 1980 $2550 1990 $5243 2000 $8653 2010 $15,919 2016 $19,488 Data from National Center for Education Statistics. 108. Race Speed At the World Championship races held at Rome’s Olympic Stadium in 1987, American sprinter Carl Lewis ran the 100-m race in 9.86 sec. His speed in meters per second after t seconds is closely modeled by the function ƒ1t2 = 11.6511 - e-t/1.272. (Data from Banks, Robert B., Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics, Princeton University Press.) (a) How fast, to the nearest hundredth, was he running as he crossed the finish line? (b) After how many seconds, to the nearest hundredth, was he running at the rate of 10 m per sec? 109. Boston Red Sox Twitter Followers The number of Twitter users (in thousands) who followed the Boston Red Sox for the years 2011 through 2018 can be modeled by the function ƒ1x2 = 2457 1 + 11.62e-0.5876x , where x represents the number of years since 2011. (Data from www.statista.com) (a) Approximately how many Twitter followers did the Boston Red Sox have in 2018? Round to the nearest thousand. (b) In what year did the Boston Red Sox have approximately 1200 thousand Twitter followers? 110. Height of the Eiffel Tower One side of the Eiffel Tower in Paris has a shape that can be approximated by the graph of the function ƒ1x2 = -301 ln x 207 , x 70, where x and ƒ1x2 are both measured in feet. (Data from Banks, Robert B., Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics, Princeton University Press.) (a) Why does the shape of the left side of the graph of the Eiffel Tower have the formula given by ƒ1-x2? (b) The short horizontal segment at the top of the figure has length 7.8744 ft. How tall, to the nearest foot, is the Eiffel Tower? (c) How far from the center of the tower is the point on the right side that is 500 ft above the ground? Round to the nearest foot. 100 100 x y f(x) = –301 ln , x+0 207 x
RkJQdWJsaXNoZXIy NjM5ODQ=