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Found in: Page 238

### Calculus

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.

See the step by step solution

## Part (a) Step 1. Explanation

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

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 $=\frac{122-121}{1}=01$

## Part (b) Step 1. Explanation

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.