522 CHAPTER 4 Inverse, Exponential, and Logarithmic Functions 78. (Modeling) Drug Level in the Bloodstream After a medical drug is injected directly into the bloodstream, it is gradually eliminated from the body. Graph the following functions on the interval 30, 104. Use 30, 5004 for the range of A1t2. Determine the function that best models the amount A1t2 (in milligrams) of a drug remaining in the body after t hours if 350 mg were initially injected. (a) A1t2 = t2 - t + 350 (b) A1t2 = 350 log1t + 12 (c) A1t2 = 35010.752t (d) A1t2 = 10010.952t 79. (Modeling) Houston Astros’ Payroll The table shows the total payroll (in millions of dollars) of the Houston Astros baseball team for the years 2014 through 2018. Year Total Payroll (millions of dollars) 2014 52.0 2015 72.5 2016 98.8 2017 124.3 2018 160.4 Data from www.baseballprospectus .com/compensation Letting ƒ1t2 represent the total payroll and t represent the number of years since 2014, we find that the function ƒ1t2 = 53.91e0.2792t models the data quite well. According to this function, when will the total payroll quadruple its 2014 value? 80. (Modeling) Transistors on Computer Chips Computing power has increased dramatically as a result of the ability to place an increasing number of transistors on a single processor chip. The table lists the number of transistors on some popular computer chips made by Intel. Year Chip Transistors 1989 486DX 1,200,000 1993 Pentium 3,100,000 2000 Pentium 4 42,000,000 2006 Core 2 Duo 291,000,000 2008 Core i7 (Quad) 731,000,000 2012 Core (3rd gen.) 1,400,000,000 2014 Core (4th gen.) 2,600,000,000 2016 Core (5th gen.) 3,200,000,000 Data from Intel. (a) Make a scatter diagram of the data. Let the x-axis represent the year, where x = 0 corresponds to 1989, and let the y-axis represent the number of transistors. (b) Decide whether a linear, a logarithmic, or an exponential function best describes the data. (c) Determine a function ƒ that approximates these data. Plot ƒ and the data on the same coordinate axes. (d) Assuming that this trend continues, use ƒ to estimate the number of transistors on a chip, to the nearest million, in the year 2020.
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