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Scientific Research: 1983–2003 The number of research articles per year, in thousands, in the prominent journal Physical Review written by researchers in Europe during 1983–2003 can be modeled by
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Applied Calculus
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- Each of Exercises 81–84 shows the graphs of the first and second derivatives of a function y = f(x). Copy the picture and add to it a sketch of the approximate graph of f, given that the graph passes through the point P.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_forwardSection 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_forward
- 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_forwardFrom its past behavior, John knows that the value of a stock has a cyclical component that increases for the first three months of each year, falls for the next 6. and rises again for the last three. In additino, inflation adds a linear component to the stock's price. John is seeking a model of the form f(t) = mt+b+Asin(pi . t/6) where t is the number of months since January 1, 2000. He has the following data: Date: Jan 1 Apr 1 Jul 1 Oct 1 Jan 1 Price: $20.00 $37.20 $33.20 $29.20 $46.40 a) Find values of m, b, and A so that f fits the data. b) During which months(s) does this stock appreciate the most?c) During which period each year is this stock actually losing value?arrow_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_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage