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Let r(t) be the rate at which the world's oil is consumed, where t is measured...
(2 points each) Answer the following multiple choice questions
by circling your answer. No justification or explanation is
required. (i) The rate at which the United States consumes oil (in
billions of barrels per year) is given by r = f(t), where t
represents the number of years since January 1, 2004. Which of the
following best describes the meaning of integral f(t) dt on the
interval [1,7].
a. The average rate of U.S. oil consumption from January 1, 2005...
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(2 points) An oil company discovered an oil reserve of 130 million barrels. For time t > 0, in years, the company's extraction plan is a linear declining function of time as follows: where q(t) is the rate of extraction of oil in millions of barrels per year at time t and b 0.05 and a -14. (a) How long does it take to exhaust the entire reserve? time years (b) The oil price is a constant 30...
3. The graphs shows the rate at which U.S. oil was produced and imported between 1920 and 2005 in units of millions of barrels per day. The total amount of oil produced or imported would therefore be the area of the region under the corresponding curve. U.S. Oil Production and Imports Use a numerical method of your choice to estimate the total amount of oil produced in the U.S. between 10 1940 and 2000. Be careful with units; time is...
Consider the extraction of oil from a well. Let x(t) be the rate of extraction in barrels per day and p(t) the price in dollars per barrel at time t. Then R(t) = pt)x(t) is the revenue in dollars per day. Find an expression for Rt), and give it an economic interpretation in the case when p() and x(1) are both increasing. (Hint: R(t) increases for two reasons...)
Daily oil production in Mexico and daily U.S. oil imports from Mexico during 2005-2009 could be approximated by P(t) 3.9 - 0.10t million barrels (5 <t<9) (t) - 2.1 0.11t million barrels (5s ts 9), where tis time in years since the start of 2000 3.5 Production 2.5 Imports 1.5 .5 5 5.5 6 6.5 77.5 8 8.5 9 (a) What are represented by the functions P) - () and Kt/P(t)? Pro-K) represents the daily production of oil in Mexico...
Let f be a function of two variables x,y. Define r(t) Yobt y(t) Хо + at, Let g(t) f(x(t), y(t)) (a) Explain what does (x(t), y(t)) represent in the plane (b) Explain how the graph of g can be viewed as a part of the graph of f. dg (c) Find dt \t=0 in terms of partial derivatives of f. What does this repre- sent? (d) What does your answer in part c become if a 0 or b=0? (e)...
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number 13
simple R/P Patlo estimate of would obviously double the 50 years. But what would it do to my 39-year estimate, which assumes a 1.3% annual growth rate in oil con- sumption? Study Box 5.3 for help with this exercise. In 2015 China consumed oil at a rate of about 11 million barrels per day, which was increasing by 8% annually The United States consumed about 19 million barrels per day, with little change from year to year....
Answer Parts a - e
Suppose that the rate of consumption of a natural resource is c'(t), where c'(t)=ke. Here t is time in years, ris a constant, and k is the consumption in the year when t = 0. In 2010, an oil company sold 1.8 billion barrels of oil. Assume that r=0.02. Complete parts a.-e. below. a. Write c'(t) for the oil company, letting t= 0 represent 2010. c'(t)= This question has not been completed. 4 parts *...
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years. Find the rate at which the balance is changing when t = 1 year, t = 10 years, and 50 years. (Round your answers to two decimal places.) (a) t-1 year per year (b) t10 years per year (c)50 years per year
The balance A (in dollars) in a savings account is given by A-7000ec, where t is measured in years....
Retail revenue each year from internet shopping is approximated by the function .TR(t)=0.075t^3+0.025t^3+2.4 where TR(t)is measured in billions of dollars andtis measured in years, with t=0 corresponding to the beginning of the year 2000. a)Find an expression giving the rate of change of the retail revenue per year from internet shopping at any timet. b)Is on-line retail revenue increasing or decreasing over time? Explain your answer.