Questions: The rate of consumption of oil in Canada during the 1990's (in billions of barrels per year) is modeled by the function 27.21 e^(t/28), where t is the number of years after January 1,1990. Find the total consumption of oil in Canada from January 1, 1990 to January 1, 2000. Round to three decimal places.

Solution Steps

To find the total consumption of oil in Canada from January 1, 1990, to January 1, 2000, we need to integrate the given rate of consumption function over the interval from \( t = 0 \) to \( t = 10 \). This will give us the total amount of oil consumed over that period. The integration of the exponential function can be done using Python's numerical integration capabilities.

The rate of consumption of oil in Canada during the 1990s is modeled by the function: \[ R(t) = 27.21 e^{\frac{t}{28}} \] where \( t \) is the number of years after January 1, 1990.

To find the total consumption of oil from January 1, 1990, to January 1, 2000, we need to evaluate the definite integral of the rate of consumption function from \( t = 0 \) to \( t = 10 \): \[ C = \int_{0}^{10} R(t) \, dt = \int_{0}^{10} 27.21 e^{\frac{t}{28}} \, dt \]

Upon evaluating the integral, we find that the total consumption of oil over the specified period is: \[ C \approx 327.029 \text{ billion barrels} \]

Final Answer