In Problems 33–36, find the associated cumulative distribution function. Graph both functions (on separate sets of axes).
34.
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Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
- 9 Draw a graph of y = f(x) such that f(-2) = 5, f(1) = 0, and f(4) = 3. %3|arrow_forward19) The following table shows the number of science research articles in a journal authored by researchers in the European Union during the period 1980–2010. Year t(year since 1980) 0 5 10 15 20 25 30 Articles N(t)(thousands) 150 190 200 260 310 350 430 (a) Find the interval(s) over which the average rate of change of N was the least positive. (Select all that apply.) 1980–2010 1980–1985 1990–1995 1985–1990 2000–2005 What was that rate of change? _______thousand articles per yearInterpret your answer. During this period, the number of articles authored by researchers in Europe increased at an average rate of____________ articles per year. (b) The percentage change of N over the interval [a, b] is defined to be Percentage change of N = Change in N First value = N(b) − N(a) N(a) . Compute the percentage change of N over the interval [10, 30]. (Round your answer to the nearest whole number.)__________ %Compute the average rate of change. (Round your answer…arrow_forward2. (a). Determine whether the Mean Value Theorem applies to f(x) = 3x + i (1,4]. %3D (b). If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.arrow_forward
- 6) The following figure shows that the probability of a plant flowering in 1987 was related to its initial size (as defined by leaf area) in 1984. Also, for a given-size plant, the probability of flowering declines as a function of previous allocation to reproduction (measured as the number of fruits produced during 1984-1986). Based on this figure, approximately how large (leaf area in cm3) would a plant that has produced three fruits over the last three years have to be in order to have an approximately 50% (0.50) probability of flowering? Probability of flowering in 1987 1.0 0.8 0.6 0.4 0.2 00000 ***** AM 100 Question 6 options: 100 cm3 150 cm3 300 cm3 250 cm3 00 .. 200 300 Leaf area in 1984 (cm²) O fruits 1 fruit ▲ 2 fruits 3 fruits 400 500arrow_forward1 3rd. 3 Beth has $10.000 invested, part_at %o and the rest at 10 % per úear. The total yearhy interest was $j90. How much 7% $7,000, 10% $3,00) 'did' She inuest at each rate?arrow_forward13. The graph of the function f is shown in the figure below. If g(x) = ] At) dt, which of the %3D following values is greatest? You will need to justify your answer. i.) g(-3) ii.) g(-2) iii.) g(0) iv.) g(1) v.) g(2)arrow_forward
- 10. Students in an accounting class took a final exam and then took equivalent forms of the exam at monthly intervals thereafter. The average score S(m), as a percent, after m months was found to be given by the function S(m) = 87 – 6 In(m + 1), m >0 (g) If it takes a 75% to pass when did the average fail below a passing score?arrow_forward1.Let X be the sum of the upfaces on a roll of a pair of fair 6-sided dice. Find F (x) and its graph. X 2.Consider again the experiment of tossing two dice.Let Y denote the absolute difference. Find F (x) and its graph. 3. Consider problems 1&2 above. Find F (x=2.5).arrow_forwardThe following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. Year 2010 2012 2014 2016 2018 2020 CO2 Emissions 339.5 361.5 399.1 425.8 452.1 495.4 Year 2022 2024 2026 2028 2030 2032 CO2 Emissions 556.2 595.9 629.7 665.1 703.1 743.7 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.) y(x) = X (b) Find the model's estimate for the 2022 data point. (Round your answer to two decimal places.) x million metric tons (c) Find the slope of the linear model. (Round your answer to two decimal places.) x Interpret the slope of the linear model. For each year since 2010 ✔ , carbon dioxide emissions in the U.S. are expected to change by x million metric tons.arrow_forward
- The following table gives the millions of metric tons of carbon dioxide emissions in a certain country for selected years from 2010 and projected to 2032. Year 2010 2012 2014 2016 2018 2020 CO2 Emissions 337.5 361.5 395.1 425.8 451.1 496.4 Year 2022 2024 2026 2028 2030 2032 CO2 Emissions 558.2 592.9 628.7 662.1 709.1 742.7 (a) Create a linear function that models these data, with x as the number of years past 2010 and y as the millions of metric tons of carbon dioxide emissions. (Round all numerical values to two decimal places.)y(x) = (b) Find the model's estimate for the 2028 data point. (Round your answer to two decimal places.) million metric tons(c) Find the slope of the linear model. (Round your answer to two decimal places.)Interpret the slope of the linear model. For each year since ---Select--- 2009 2010 2015 2028 2032 , carbon dioxide emissions in the U.S. are expected to change by million metric tons.arrow_forward10. Students in an accounting class took a final exam and then took equivalent forms of the exam at monthly intervals thereafter. The average score S(m), as a percent, after m months was found to be given by the function S(m) = 87 – 6 In(m + 1), m > 0 (a) What was the average score when the students initaially took the test, m = = 0? (b) What was the average score after 1 month? (c) What was the average score after 6 months?arrow_forward1. Suppose C(x) is a function representing the cost (in dollars) of producing x units of energy, and R(x) is a function representing the revenue (in dollars) of selling x units of energy. Suppose further that both functions are continuous for all x > = 0. A. Is there necessarily some x value, let's call it C, that will maximize profit over all x > = 0? Explain your answer. %3D B. Suppose we know we can't produce more than 1,000 units of energy. Is there necessarily some x-value, call it C, that will maximize profit over the interval [0,1000]? Explain your answer. C. Again, assume that we can't produce more than 1,000 units of energy. Is there necessarily some x value, let's call it C, for which the profit is exactly 0? Explain your answer. 2. Produce a function f(x) that satisfies the following conditions: A. I. Its domain is all real numbers. II. It has no maximum and no minimum on the interval [ 1,3] . III. It satisfies f(1) = 1 and f(3) = -1, but there does not exist ac between 1…arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,