An oil well Produces oil at a rate of ft 121 t2 Where t is

An oil well Produces oil at a rate of f(t) = 121 - t^2. Where t is in years and the rate f(t) is in thousands of barrels. a) How long until the oil well does not produce any more oil? b) What was the total Production output for all those years when it still produced oil?

Solution

The oil well stops producing when the rate of production reaches equal to zero .

=> f(t) = 0

=> 121 - t² = 0

=> t = 11 years

Total Oil production , F(t) = ₀^t f(t) . dt

F(t) = ₀¹¹ ( 121 - t² ) dt = 2662/3 thousand barrels