Concept explainers
GDP Use the following information to answer Exercises 47–50. The gross domestic product (GDP; in tens of trillions of U.S. dollars) for China and the United States can be approximated as follows:
where
If the trend continues, what is the first full year in which China’s GDP surpasses $25 trillion?
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Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
- In cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W, which is supposed to predict how cold we will feel for a given air temperature T, in degrees Fahrenheit, and wind speed V, in miles/hour. The National Weather Service uses the following formula: W=35.74+0.6215T−35.75V^0.16+0.4275TV^0.16, for T≤50 and V≥3. What is the wind chill index when the air temperature is 25 degrees and the wind speed is 18 miles/hour?Answer: Calculate the partial derivatives WT and WV when T=25 and V=18.WT= WV= Use your answer above to do the following question: When the air temperature is 25 degrees, estimate the change in the wind chill index if the wind speed increases by 2 miles/hour from 18 miles/hour.Answer:arrow_forwardQI. Find ý of the function x2 - e2x+3y - In(xy) = 0. %3Darrow_forwardShow workarrow_forward
- Life expectancy is the key metric for assessing population health. The following graph shows the life expectancy for the United States and Africa between the years 1970 and 2020. Let U(t) represent the life expectancy (in years) in the United States and A(t) represent the life expectancy (in years) in Africa, where t is the number of years since 1970. Life Expectancy in Years 739 N NI N na 9 S United States 70 Atrica SL4 SA 47.7 40 190 1995 190 195 1990 1995 2000 200s 2010 201s 2020 Year Evaluate (U - A) (20) and give a practical interpretation. O (U - A) (20) = -14.0 In 2020, the life expectancy in the United States was 14.0 years less than the life expectance in Africa. O (U - A) (20) = 23.1 In 1990, the life expectancy in the United States was 23.1 years more than the life expectancy in Africa. None of these O (U – A) (20) = -23.1 In 1990, the life expectancy in the United States was 23.1 years less than the life expectancy in Africa. O (U - A) (20) = 14.0 In 2020, the life…arrow_forwardsection 14.4 question 7arrow_forwardWorld Population The low long-range world population numbers and projections for the years 1995–2150 are given by the equation y = -0.00036x2+0.0385x + 5.823, where x is the number of yearsafter 1990 and y is in billions. During what yearsdoes this model estimate the population to be above6 billion?arrow_forward
- I need help with this question.arrow_forwardA tank is discharging water through an orifice at a depth x (m) below the surface of water whose area A (m²). The following are the values of the (corresponding values of (A) w.r.t (x : x (m) 1.5 1.65 1.8 1.95 2.10 225 24 255 27 2.85 3 A (m) 125 139 1.52 1.65 181 1.96 212 229 246 2.65 2.83 :Using the following formula 3.0 A dx T = 1.5 Calculate (T) for the level of water to drop from 1.5 m to 3 m by .Simpson's 1/3 rulearrow_forward(f) In earrow_forward
- From 1950 through 2005, the per capita consumption C of cigarettes by Americans (age 18 and older) can be modeled by C = 3565.0 + 60.30t − 1.783t2, 0 ≤ t ≤ 55, where t is the year, with t = 0 corresponding to 1950. In 2005, the U.S. population (age 18 and over) was 296,329,000. Of those, about 59,858,458 were smokers. What was the average annual cigarette consumption per smoker in 2005? What was the average daily cigarette consumption per smoker?arrow_forwardMedical studies of obesity use the Body Mass Index (BMI), which is defined by w BMI = where w is weight in kilograms and h is height in meters. (a) Using the fact that 1 kg = 2.2 lb and 1 meter = 39.4", calculate the BMI of a 5'5" woman who weighs 150 lb. (b) Which has more effect on the BMI: a 10% weight increase or a 10% height decrease? Justify your answer.arrow_forwardExercise 5.2.9. Suppose G≈ H. Show Z(G) ≈ Z(H).arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage