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Expert-verifiedFound in: Page 238

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Rates of change from data: The following table lists the consumption of gasoline in billions of gallons in the United States from 1994 to 2000:

(a) Compute the average rate of change in gasoline consumption in the United States for each year from 1994 to 2000.

(b) During which year was gasoline consumption increasing most rapidly? Least rapidly? Estimate the instantaneous rates of change in gasoline consumption during those years.

Part (a) In 1995, rate of change $=2$

In 1996, rate of change $=2$

In 1997, rate of change $=4$

In 1998, rate of change $=1$

In 1999, rate of change $=3$

In 2000, rate of change $=1$

Part (b) The year during which gasoline consumption increasing most rapidly is 1997.

The years during which gasoline consumption increasing least rapidly are 1998 & 2000.

It is known that average rate of change is determined by $\frac{\u2206y}{\u2206x}i.e.\frac{changeiny}{changeinx}$

Now,

In 1995, rate of change $=\frac{111-109}{1}=02$

In 1996, rate of change $=\frac{113-111}{1}=02$

In 1997, rate of change $=\frac{117-113}{1}=04$

In 1998, rate of change $=\frac{118-117}{1}=01$

In 1999, rate of change $=\frac{121-118}{1}=03$

In 2000, rate of change $=\frac{122-121}{1}=01$

From part (a)

In 1995, rate of change $=02$

In 1996, rate of change $=02$

In 1997, rate of change role="math" localid="1660815174706" $=04$

In 1998, rate of change $=01$

In 1999, rate of change $=03$

In 2000, rate of change $=01$

The year during which gasoline consumption increasing most rapidly is 1997.

The years during which gasoline consumption increasing least rapidly are 1998 & 2000.

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