An oil well is expected to produce oil at the rate of $54 e^{- 0.05 t}$ thousand barrels per month indefinitely, where $t$ is the number of months that the well has been in operation. Find the total output (in barrels) over the lifetime of the well by integrating this rate from 0 to $c$ . [Note: The owner will shut down the well when production falls too low, but it is convenient to estimate the total output as if production continued forever.]

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An oil well is expected to produce oil at the rate of

54 e^{- 0.05 t}

thousand barrels per month indefinitely, where

t

is the number of months that the well has been in operation. Find the total output (in barrels) over the lifetime of the well by integrating this rate from 0 to

c

. [Note: The owner will shut down the well when production falls too low, but it is convenient to estimate the total output as if production continued forever.]

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