An oil company discovered an oil reserve of 110 million barrels. For time t > 0, in years, the company's extraction plan is a linear declining function of time as follows:q(t) = a – bt,where g(t) is the rate of extraction of oil in millions of barrels per year at time t and b = 0.05 and a = 10.(a) How long does it take to exhaust the entire reserve?time =years(b) The oil price is a constant 30 dollars per barrel, the extraction cost per barrel is a constant 16 dollars, and the market interest rate is 9 percent per year, compounded continuously.What is the present value of the company's profit?value =millions of dollars

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Answered: An oil company discovered an oil…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The total expenditures (in millions) of current dollars for pollution abatement and control during the poriod from 2000 through 2019 can be approximatod by the function P(x) = 175.17 e008x, where x0 corresponds to the year 2000. (a) In what year would the total expenditures reach $209 million dollars? (b) If this model remains accurate, when would the total expenditures reach $481 million?
A tank holds 200 gal of water that contains 40 lb of dissolved salt. A brine (salt) solution is flowing into the tank at the rate of 2 gal per minute while the solution flows out at the same rate. The brine solution entering the tank has a salt concentration of 4 lb per gal. (a) Find a function that represents the amount of salt in the tank at any time. (b) As time passes, what happens to the salt concentration?
The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 through 2019 can be approximated by the function P(x) = 166.61 e 0.03x, where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $208 million dollars? (b) If this model remains accurate, when would the total expenditures reach $482 million? (a) The expenditures would reach $208 million in the year mid- (Simplify your answer. Type a whole number.)
In 2010, the population of a country was 53 million and growing at a rate of 1.7% per year. Assuming the percentage growth rate remains constant, express the population, P, in millions, as a function of t, the number of years after 2010. P = f(t) = [ million people help (formulas)
According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year. Assuming this growth rate continues, the model t- 2008 P(t) = 304 · (1.011)' represents the population P (in millions of people) in year t. According to the model, when will the population be 442 million people? Be sure to round your answer to the nearest whole year. Year
A large tank has a capacity of 300 gallons. Initially, the tank contains a brine solution of 200 gallons with 40 pounds of dissolved salt. A solution with a concentration of 4 pounds of salt per gallon is admitted into the tank and the well-stirred solution is withdrawn from the tank at a rate of 2 gallons per minute. a) Find the function (1) where y(1) represents the number of pounds of salt in the tank at f minutes. Give exact values here. b) Find the number of pounds of salt in the tank when the tank is completely full. Express your answer as a decimal with 1 decimal place accuracy.
The growth of outpatient surgeries as a percent of total surgeries at hospitals is approximated by f(x) =D - 1313 +305 In x where x is the number of years since 1900. (a) What does this function predict for the percent of outpatient surgeries in 1995? (b) When did outpatient surgeries reach 40%? (a) What does this function predict for the percent of outpatient surgeries in 1995? % (Round to the nearest percent as needed.) (b) When did outpatient surgeries reach 40%? st 2 (Round down to the nearest year.) - Test 3

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