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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

The table shows world average daily oil consumption from 1985 to 2010 measured in thousands of barrels per day.

(a) Compute the interpret the average rate of change from 1990 to 2005. What are its units?

(b) Estimate the instantaneous rate of change in 2000 by taking the average of two average rates of change. What are its units?

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(a)

To determine

To find: The average rate of change from 1990 to 2005 and state the interpretation. Then describe the units for the average rate of change ΔCΔt.

Explanation

Given:

Let C(t) be the average daily consumption of oil measured in thousands of barrel per day with respect to time, where t is in years.

The table of average daily consumption of oil (in thousands of barrel per day) with respect to time t is given below.

t (in years)C(t) (in thousands of barrels per day)
198560,083
199066,533
199570,099
200076,784
200584,077
201087,302

Formula used:

The average rate of change of C with respect to t on the interval [t1,t2] is,

ΔCΔt=C(t2)C(t1)t2t1 (1)

Calculation:

Obtain the average rate of change of C(t) from 1990 to 2005

(b)

To determine

To estimate: The instantaneous rate of change of C(t) in t=2000 and find its units.

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