One way to describe the change in a quantity over time is to
calculate *absolute (*or *total)
change*. To find this number, subtract the new quantity from the
original quantity.

**Example 1**: On
September 20, a gallon of gas at my usual gas station cost $1.83. On September 30, I noticed that the
price had gone down to $1.65 per gallon.

The absolute change in the price of gas between September 20 and September 30 is

* 1.65
Ð 1.83 = - 0.18 dollars per gallon*

We say that the price of gas *decreased* by $0.18 (or 18 cents). Notice that when we use the word Òdecreased,Ó we donÕt need
to use the negative in front of the number.

**Example 2**: Last
month, I paid $1.99 per gallon of heating oil. This month, when I got my bill, I saw that the price was
$2.10 per gallon.

The absolute change in the price of heating oil during that month was

* 2.10
Ð 1.99 = 0.11 $ per gallon*

We say that the price of heating
oil *increased* by 11 cents that month.

You can also use *percentage change *to* *describe
change. To calculate the
percentage change: find the absolute change, then divide that number by the original amount. To turn your answer into a percentage,
multply by 100.

*Percentage change = absolute change (100)*

**Example 1 revisited:** On
September 20, a gallon of gas at my usual gas station cost $1.83. On September 30, I noticed that the
price had gone down to $1.65 per gallon.

The percentage change in the price of gas between September 20 and September 30 is

__(1.65
Ð 1.83__) 100 = - 0.18(100) = -18% per gallon

*
1.83*

We say that the price of gas *decreased* by 18% per gallon.

**Example 2 revisted**: Last
month, I paid $1.99 per gallon of heating oil. This month, when I got my bill, I saw that the price was
$2.10 per gallon.

The percentage change in the price of heating oil is:

* ( 2.10
Ð 1.99) 100 = (0.055)100 =
5.5% per gallon*

* 1.99*

We
say that the price of heating oil *increased*
by 5.5% per gallon.

**Summary**: Let *a* be the original
quantity and *b* be the new quantity.

**absolute change** between the
quantities is *b Ð a*.**percentage** **change** between the quantities is *( b Ð a )100*.

*
a*

**Practice problems**

1. In 1950, the world population was estimated to be 2,520,000,000. By 1980, the population had increased to 4,440,000,000.

a) find the absolute change in world population between 1950 and 1980. Write your answer in a complete sentence.

b) find the percentage change in world population between 1950 and 1980. Write you answer in a complete sentence.

c) If you were writing an analysis of world population change, which number would make a more dramatic point: the absolute change or the percentage change? Explain your answer.

For the rest of the problems, find the absolute change and the percentage change. In your opinion, which number is better expresses change for that particular problem? Circle your answer in each case.

2. During the past two years, median household income for families living in the Midwest went from $44,531 to 43,622.

3. The census Bureau reported that the number of Americans without health insurance grew from 41.4 million in 2002 to 43.6 million in 2003.

4. UMass Boston tuition cost per credit (not counting fees) was 79.50 in 1988. In 2004 the per credit tuition is $71.50.

5. Undergraduate enrollment at UMass Bostion was 10,071 in 2002, down from 10,656 in 2001.

6. In fiscal year 2001 UMass Boston received $85.6 million from the State, compared to $60.7 million this year (fiscal year 2004).