Bottled Water Sales (Compare Exercise 46 in Section 6.3.) The rate of U.S. per capita sales of bottled water for the period 2007–2014 can be approximated by
where t is time in years since the start of 2007. Use a definite
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Chapter 6 Solutions
Applied Calculus
- the population P (in millions) in Russian from 1996 to 2004 can be approximated by the model P=152.26e-0.00039t where t=6 represents the year 1996. using the model, and without doing any calculations. answer the following question. would the population of Russian be increasing or decreasing during the given time period? explain.arrow_forwardDisposable income is the amount available for spending and saving after taxes have been paid and is one gauge for the state of the economy. Using U.S. Energy Administration data for selected years from 2010 and projected to 2040, the total U.S. disposable income, in billions, can be modeled by D = 10,020e0.02292t where t is the number of years past 2010. In what year is disposable income predicted to be $18 trillion (that is, $18,000 billion)?arrow_forwardTHe rate of U.S. per capita sales of bottledwater for the period 1993–2003 could be approximated by Q(t) = 0.05t^2 + 0.4t + 9 gallons per year (3 ≤ t ≤ 13) where t is the time in years since 1990.Use the FTC to estimate the total U.S. per capita sales of bottled water from 1995 to 2000. (Round your answer to the nearest gallon.)arrow_forward
- model a population p if its rate of growth is proportional to the amount present at time tarrow_forwardthe population P (in millions) in Russian from 1996 to 2004 can be approximated by the model P=152.26e-0.00039t where t=6 represents the year 1996. using the model, and without doing any calculations. answer the following question. would the population of Russian be increasing or decreasing during the given time period? explain. given the model continues to be relevant to the population, predict the population of Russia in the year 2020.arrow_forwardSales of milk at time t years are projected to be at the rate of 15 + 30e-0.5t million gallons per year. Find total sales in the next ten years.arrow_forward
- The capacities at which U.S. nuclear power plants are working are shown in table for various years. Year Percent 1975 56 1980 59 1985 58 1990 70 1995 76 2000 88 2004 89 Let f(t) be the capacity (in percent) at which U.S. nuclear power plants are working at t years since 1970. A model of the situation is f(t)=0.027t^2+0.216t+53.296 Estimate at what capacity U. S. nuclear power plants were working in 2008? (Round to the nearest whole percent) % Predict when U. S. nuclear power plants will be working at full (100%) capacity? (Enter the year this occurs.)arrow_forwardSuppose that 40 deer are introduced in a protected area. The population of the herd P can be modeled by P = 40 + 20x / 1 + .05x where x is the time in years since introducing the deer. Determine the time required for the deer population to reach 200.arrow_forwardThe air in a room with volume 180 m3 contains 0.15% carbondioxide initially. Fresher air with only 0.05% carbondioxide flows into the room at a rate of 2 m3/min and themixed air flows out at the same rate. Find the percentageof carbon dioxide in the room as a function of time. Whathappens in the long run?arrow_forward
- 3. After long study, tree scientists (dendrologists) conclude that a eucalyptus tree will grow at a rate of 0.6 + 4 feet per year, where t is time in (1+1) years. a. Find the number of feet that the tree will grow in the second year.arrow_forwardFish enter a lake at a rate modeled by the function Earrow_forwardproblen 1.2arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage