The price of crude oil during the period 2000-2010 can be approximated by P(f) =

Question

The price of crude oil during the period 2000-2010 can be approximated by P(f) = 6t+ 18 dollars per barrel (0 lessthanorequalto t lessthanorequalto 10) In year t, where t = 0 represents 2000. Russia's crude oil production over the same period can be approximated by Q(t) = -0.08t^2 + 1.2t + 5.5 million barrels per day (0 lessthanorequalto t lessthanorequalto 10). Use these models to estimate Russia's daily oil revenue and also its rate of change in 2008. (Round your answers to the nearest $1 million, dally oil revenue $ million rate of change In 2008 $ million per year

Explanation / Answer

P(t) = 6t + 18

Q(t) = -0.08t^2 + 1.2t + 5.5

R(t) = P(t) * Q(t) = (6t + 18)(-0.08t^2 + 1.2t + 5.5) = -0.48t^3 + 5.76t^2 + 54.6t + 99

For year 2008, t = 8

R(8) = -0.48(8)^3 + 5.76(8)^2 + 54.6(8) + 99 = $658.68 million (Answer: 659 million)

R'(t) = -1.44t^2 + 11.52t + 54.6

R'(8) = -1.44(8)^2 + 11.52(8) + 54.6 = $54.6 million per year.

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