Suppose that the rate of consumption of a natural resource is c prime left parenthesis t right parenthesisc′(t), where c'(t)=k ert. Here t is time in years, r is a constant, and k is the consumption in the year when tequals=0. In 2010, an oil company sold 1.7 billion barrels of oil. Assume that requals=0.02. Complete parts a.-e. below. A. Write c ′(t) for the oil company, letting t=0 represent 2010.
B. Set up a definite integral for the amount of oil that the company will sell in the next 10 years.
C. Evaluate the definite integral of part b. Evaluating the definite integral gives billion barrels of oil.
D. The company has about 20 billion barrels of oil in reserve. To find the number of years that this amount will last, solve the equation Integral from 0 to Upper T (1.7 e 0.02 t dt = 20
E. Rework part assuming that requals=0.010.01.