Question

Read Explain 3 Parts A and B and complete Your Turn #8 below (adapted from Lesson 6.1).

8.
According to the data from the U.S. Census Bureau for 1990-2009, the number of
commercially owned automobiles in the United States can be modeled by the function
A(x) = 1.4x – 130.6x² + 1831.3x + 128,141, where x is the number of years after 1990
and A(x) is the number of automobiles in thousands. The number of privately-owned
automobiles in the United States can be modeled by the function
P(x) = -x + 24.9x² – 177.9x + 1709.5, where x is the number of years after 1990 and
P(x) is the number of automobiles in thousands. Estimate the total number of automobiles
owned in 2005.

Answer 1

Answer: 130875 automobiles

Explanation:

To estimate the total number of automobiles owned in 2005, let's first find the number of years

2005 - 1990 = 15 years

Given that the Commercially owned automobiles in the United States can be modeled by the function

A(x) = 1.4x – 130.6x² + 1831.3x + 128,141, where x is the number of years after 1990

and A(x) is the number of automobiles in thousands.

Substitute 15 for x in the function

A(x) = 1.4(15) – 130.6(15)² + 1831.3(15) + 128,141

A(x) = 21 - 29385 + 27469.5 + 128141

A(x) = 126246.5 automobiles

The number of privately-owned automobiles in the United States can be modeled by the function

P(x) = -x + 24.9x² – 177.9x + 1709.5, where x is the number of years after 1990

Substitute 15 for x in the function

P(x) = -(15) + 24.9(15)² – 177.9(15) + 1709.5

P(x) = -15 + 5602.5 - 2668.5 + 1709.5

P(x) = 4628.5 automobiles

The total automobile = A(x) + P(x)

Substitutes for A(x) and P(x)

The total automobile = 126246.5 + 4628.5

= 130875

Therefore, the total number of automobiles owned in 2005 is 130875 automobiles