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Scientific Research: 1983–2003 The percentage of research articles in the prominent journal Physical Review written by researchers in the United States during 1983–2003 can be modeled by
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Applied Calculus
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- The U.S. Department of Health and Human Services provides a summary of the number and rate of abortions for the period 1990–2006. Based on these data, the United States abortion rate (number of abortions per 1000 women) can be estimated by the linear function R(x) = −0.58x + 23.9 where x is the year since 1990 and R(x) is the abortion rate. (a) Based on this function, is the rate increasing or decreasing? The slope is , so the rate is . (b) Find the estimated abortion rate for 2007 and for 2017. 2007 abortions per 1000 women 2017 abortions per 1000 women (c) Estimate the year when the abortion rate will be 10. (Round your answer to the nearest year.)arrow_forward2) The Nikkei 225 index is a stock market index for the Tokyo Stock Exchange. The Nikkei 225 index for the period 1990-2010 can be modeled by V (t) = 23,500e-0.0381t where t is the number of years after 1990. Determine how many years after 1990 the Nikkei 225 index reached $20,000.arrow_forwardWhich of the functions graphed in Exercises 1–6 are one-to-one, and which are not?arrow_forward
- Section 7.2: 1. Starting in 2018 (t = 0), the rate at which oil is consumed by a small country increases at a rate of 1.5% per year, starting with an initial rate of 1.2 million barrels/year. a) How much oil is consumed over the course of the year 2018 (between t =0 and t 1)? b) Find the function that gives the amount of oil consumed between t = 0 and any future time t. %3D c) How many years after 2018 will the amount of oil consumed since 2018 reach 10 million barrels?arrow_forwardIn Exercises 49–52, find an equation for and sketch the graph of the level curve of the function ƒ(x, y) that passes through the given point.arrow_forwardIn the section opener, we saw that 80x – 8000 f(x) 30 s xs 100 110 models the government tax revenue, f(x), in tens of billions of dollars, as a function of the tax rate percentage, x. Use this function to solve Exercises 55–58. Round to the nearest ten billion dollars. 55. Find and interpret f(30). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 56. Find and interpret f(70). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 57. Rewrite the function by using long division to perform (80x - 8000) - (x - 110). Then use this new form of the function to find f(30). Do you obtain the same answer as you did in Exercise 55? Which form of the function do you find easier to use? 58. Rewrite the function by using long division to perform (80x – 8000) - (x – 110).arrow_forward
- The table shows data for sulfur dioxide emissions from electricity generation (in millions of short tons) for selected years from 2000 and projected to 2035. These data can be modeled by the function E(x) = (0.001x - 0.062)(-0.18x2 + 8.2x - 200) where x is the number of years past 2000. Short Tons Year (in millions) 2000 11.4 2005 10.2 2008 7.6 2015 4.7 2020 4.2 2025 3.8 2030 3.7 2035 3.8 (a) Find the function that models the rate of change of these emissions. (Use exact numerical values. Do not round.) E'(x) = (b) Find E'(15). (Give an exact answer. not round.) E'(15) =arrow_forwardThe table shows data for sulfur dioxide emissions from electricity generation (in millions of short tons) for selected years from 2000 and projected to 2035. These data can be modeled by the function E(x) = (0.001x - 0.062)(-0.18x2 + 8.2x - 200) where x is the number of years past 2000. Short Tons Year (in millions) 2000 11.4 2005 10.2 2008 7.6 2015 4.7 2020 4.2 2025 3.8 2030 3.7 2035 3.8 (a) Find the function that models the rate of change of these emissions. (Use exact numerical values. Do not round.) E'(X) = (0.001x – 0.062)[2(-0.18)x+ 8.2] + (–0.18x² + 8.2x – (b) Find E'(20). (Give an exact answer. Do not round.) E'(20) = 0 Interpret E'(20). O In 2020, emissions from electricity generation will be increasing. O In 2020, emissions from electricity generation will be constant. O In 2020, emissions from electricity generation will be decreasing.arrow_forwardIn Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!arrow_forward
- . Subprime Mortgage Debt during the Housing Bubble (Compare Exercise 104.) During the real estate run-up 2000–2008 the value of subprime (normally classified as risky) mortgage debt outstanding in the United States could be approximated by in 1,350 A(t) = 1 + 4.2(1.7) billion dollars (0arrow_forwardPoint A is launched horizontally away from a wall and a(t) represents Point A's distance from the wall (in meters) in terms of the number of seconds t since the point was launched. Point B is also launched from the wall, but travels 2.5 times as fast as Point A. A Click here to launch the points. a. Suppose b(t) represents Point B's distance from the wall (in meters) in terms of the number of secondst since the points were launched. Write a function formula for b using the function a. b(t) = Preview b. The graph of function a is shown below (in black). Sketch the graph of function b. 20 16 12 8. 4 1 3 4 5 Clear All Draw:arrow_forwardThe populations P (in thousands) ofHorry County, South Carolina, from 1971 through 2014can be modeled byP = 76.6e0.0313twhere t represents the year, with t = 1 corresponding to1971. (Source: U.S. Census Bureau)(a) Use the model to complete the table. (b) According to the model, when will the populationof Horry County reach 360,000?(c) Do you think the model is valid for long-termpredictions of the population? Explain.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage