Year 2003 2004 2005 2006

Populatation 22.12 22.49 22.86 23.41

A. divide the population for each year by the population in the preceeding year. Round to the two decimal places and show the Texas population increase that is approximately geometric.

1.01
B. Write the general term of the geometric sequence modeling texas population in millions n years in 2002.

an= 22.12 (1.01)n-1

C. Use your model from part (b) to project texas's population in millions for the year 2010. round to two decimal places.

approximately 26.4

To answer these questions, we need to understand the concept of a geometric sequence and how to calculate it.

A geometric sequence is a sequence of numbers in which each term is found by multiplying the preceding term by a constant factor, called the common ratio. In this case, we need to calculate the geometric increase in the Texas population.

A. To find the population increase that is approximately geometric for each year, we need to divide the population for each year by the population in the preceding year. Let's calculate it for each year:

- For 2004: 22.49 / 22.12 = 1.0168 (rounded to two decimal places)
- For 2005: 22.86 / 22.49 = 1.0165 (rounded to two decimal places)
- For 2006: 23.41 / 22.86 = 1.024

So, the population increase that is approximately geometric for each year is as follows: 1.01, 1.02, 1.02.

B. The general term of a geometric sequence is usually represented as an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number.

In this case, the first term (a1) is 22.12 (from the year 2003), and the common ratio (r) is 1.01 (rounded from the previous calculations). Therefore, the general term for the Texas population in millions n years in 2002 is:

an = 22.12 * (1.01)^(n-1)

C. To project Texas's population in millions for the year 2010, we need to calculate the value of a10 (as n = 2010 - 2002 = 8).

Using the general term from part (B), let's plug in n = 8:

a10 = 22.12 * (1.01)^(8-1) = 26.43 (rounded to two decimal places)

So, the projected population for the year 2010 is approximately 26.43 million.