(a)
(b)
(c)
(a)
(b)
(c)
Figure N6–15cExample 33 __
Assume the world use of copper has been increasing at a rate given by f(t) =
15 e0.015t, where t is measured in years, with t = 0 the beginning of 2000, and f(t)
is measured in millions of tons per year.
What definite integral gives the total amount of copper that was used for the
5-year period from t = 0 to the beginning of the year 2005?
Write out the terms in the left sum L(5) for the integral in (a). What do the
individual terms of L(5) mean in terms of the world use of copper?
How good an approximation is L(5) for the definite integral in (a)?SOLUTIONS:
.
L(5) = 15e0.015 · 0 + 15e0.015 · 1 + 15e0.015 · 2 + 15e0.015 · 3 + 15e0.015 · 4 . The
five terms on the right represent the world’s use of copper for the 5 years
from 2000 until 2005.
The answer to (a), using our calculator, is 77.884 million tons. L(5) = 77.301
million tons, so L(5) underestimates the projected world use of copper during
the 5-year period by approximately 583,000 tons.