Chapter 8.1, Problem 21E

To determine

To calculate: the total consumption of oil in the United States from January 1, 1980, to January 1, 1990.

Answer to Problem 21E

The total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 332.965 billion of barrels.

Explanation of Solution

Given information:

The rate of consumption of oil is modelled by the function $C=27.08\cdot e^{\frac{t}{25}}$

Calculation:

Seek the cumulative effect of the consumption rate for $0\le t\le 10$

The amount consumed during this interval is approximately

  $\begin{array}{l}{\displaystyle \sum C\left(t_k\right)\Delta t\text{ billion of barrels}}\\ {\displaystyle \underset{0}{\overset{10}{\int }}C\left(t\right)dt=}{\displaystyle \underset{0}{\overset{10}{\int }}(27.08\cdot e^{\frac{t}{25}})dt}\text{ billion of barrels}\\ {\displaystyle \underset{0}{\overset{10}{\int }}C\left(t\right)dt=}27.08\cdot 25e^{\frac{t}{25}}{]}_0^{10}\text{ billion of barrels}\\ {\displaystyle \underset{0}{\overset{10}{\int }}C\left(t\right)dt=}27.08\cdot 25\left(e^{0.4}-e^0\right)\text{ billion of barrels}\\ {\displaystyle \underset{0}{\overset{10}{\int }}C\left(t\right)dt\approx }332.965\text{ billion of barrels}\end{array}$

Therefore,

The total consumption of oil in the United States from January 1, 1980, to January 1, 1990 is approximately 332.965 billion of barrels.