A town has a population of 32,000 in the year 2002; 35,200 in the year 2003; 38,720 in the year 2004; and 42,592 in the year 2005. If this pattern continues, what will the population be in the year 2016?

Consider the increase per year:

2002-2003: 3200 factor of 1.100
2003-2004: 3520 factor of 1.100
2004-2005: 3872 factor of 1.100

This is obviously a geometric series. The population increases 10% per year, like compound interest. After 14 years (if the trend continues) , the population is
(1.1)^14*32000 = 121,520

To find the population in the year 2016 based on the given pattern, we need to calculate the growth rate per year.

Step 1: Find the growth rate
The growth rate can be calculated by dividing the population in one year by the population in the previous year.

Growth rate for 2002 to 2003 = (35,200 - 32,000) / 32,000 = 3,200 / 32,000 = 0.1 = 10%
Growth rate for 2003 to 2004 = (38,720 - 35,200) / 35,200 = 3,520 / 35,200 = 0.1 = 10%
Growth rate for 2004 to 2005 = (42,592 - 38,720) / 38,720 = 3,872 / 38,720 = 0.1 = 10%

Step 2: Calculate the population in 2016
To calculate the population in 2016, we will apply the growth rate to the population in 2015.

Population in 2005 = 42,592
Population in 2006 = 42,592 + (42,592 * 10%) = 42,592 + 4,259.2 = 46,851.2

Following the pattern, we can conclude that the population in 2016 will be approximately 46,851.

To find the population in the year 2016, we need to continue the given pattern.

First, let's calculate the difference in population between consecutive years:
- From 2002 to 2003, the population increased by 35,200 - 32,000 = 3,200.
- From 2003 to 2004, the population increased by 38,720 - 35,200 = 3,520.
- From 2004 to 2005, the population increased by 42,592 - 38,720 = 3,872.

Based on the given pattern, the population increases by 3,200, 3,520, and 3,872 in consecutive years.

Now, let's find the difference between 2015 and 2016. Since the given pattern continues, the difference in population between consecutive years would also be 3,872.

To find the population in the year 2016, add the difference (3,872) to the population in 2015:
42,592 + 3,872 = 46,464.

Therefore, the population in the year 2016 will be 46,464.