Intermediate Algebra (11th edition)

Solve each problem. See Example 6.

43.Sales of digital cameras in the United States (in millions of dollars) between 2000 and
2006 are shown in the table. In the year column, 0 represents 2000, 1 represents 2001, and
so on.

SECTION 9.5 Graphs of Quadratic Functions 539

Source:Consumer

Electronics Association.

Year Sales

0 1825

1 1972

2 2794

3 3921

4 4739

5 5611

6 7805

(a)Use the ordered pairs (year, sales) to make a scatter diagram of the data.

(b)Use the scatter diagram to decide whether a linear or quadratic function would better

model the data. If quadratic, should the coefficient aof be positive or negative?

(c)Use the ordered pairs 0, 1825 , 3, 3921 , and 6, 7805 to find a quadratic function

that models the data. Round the values of a, b, and cin your model to the nearest

tenth, as necessary.

(d) Use your model from part (c) to approximate the sales of digital cameras in the

United States in 2007. Round your answer to the nearest whole number (of millions).

(e)Sales of digital cameras were $6517 million in 2007. Based on this, is the model valid

for 2007? Explain.

44.The number (in thousands) of new, privately owned housing units started in the United
States is shown in the table for the years 2002 – 2008. In the year column, 2 represents
2002, 3 represents 2003, and so on.

1 2 1 2 1 2

x^2

Source:U.S. Census Bureau.

(a)Use the ordered pairs (year, housing starts) to make a scatter diagram of the data.

(b)Would a linear or quadratic function better model the data?

(c)Should the coefficient aof in a quadratic model be positive or negative?

(d)Use the ordered pairs 2, 1700 , 4, 1960 , and 7, 1360 to find a quadratic function

that models the data. Round the values of a, b, and cin your model to the nearest

whole number, as necessary.

(e)Use your model from part (d) to approximate the number of housing starts during 2003

and 2008 to the nearest thousand. How well does the model approximate the actual

data from the table?

1 21 2 1 2

x^2

Year Housing Starts

(thousands)

2 1700

3 1850

4 1960

5 2070

6 1800

7 1360

8 910