Question

An oil well is expected to produce oil at the rate of R'(t) = 40e^{-0.05t} 0 ? t ? 48 measured in thousand of barrels per month, where t is the number of months that the well has been in operation. Find the total output over the first 2 years. Leave your answer in exact form.

          An oil well is expected to produce oil at the rate of
R'(t) = 40e^{-0.05t} 0 ? t ? 48
measured in thousand of barrels per month, where t is the number of months that the well has been in operation. Find the total output over the first 2 years. Leave your answer in exact form.

An oil well is expected to produce oil at the rate of
R'(t) = 40e^-0.05t 0 ? t ? 48
measured in thousand of barrels per month, where t is the number of months that the well has been in operation. Find the total output over the first 2 years. Leave your answer in exact form.

Added by Brittany T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/27/2023

Step 1

We can do this by integrating the rate of production function R(t) over the interval [0, 24]: ∫[0,24] 40e^(0.05t) dt To integrate this function, we can use the substitution u = 0.05t, du/dt = 0.05, dt = du/0.05: ∫[0,1.2] 40e^u (1/0.05) du Show more…

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An oil well is expected to produce oil at the rate of R'(t) = 40e^{-0.05t}, 0 ≤ t ≤ 48, measured in thousand of barrels per month, where t is the number of months that the well has been in operation. Find the total output over the first 2 years. Leave your answer in exact form.