Question

A middle school keeps track of its population. In 2011, the school population was 1500 students. In 2012, the student population had increased by 10%. In 2013, the student population had decreased by 10%. Andy believes that the 2013 student population is the same as the 2011 student population since the population both increased and decreased by the same percentage. Identify and explain the flaw in Andy's reasoning. Determine the percent change in the number of students from 2011 to 2013.

Answer 1

Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. The percent change in the number of students from 2011 to 2013 is a 1% decrease.

Step-by-step explanation:

Andy's reasoning is flawed because the percentage increase and percentage decrease do not result in the same net change in population. Let's calculate the population in 2012 after a 10% increase. 10% of 1500 students is 150 students. So the population in 2012 would be 1500 + 150 = 1650 students.

Now, let's calculate the population in 2013 after a 10% decrease from 1650 students. 10% of 1650 students is 165 students. So the population in 2013 would be 1650 - 165 = 1485 students.

To determine the percent change in the number of students from 2011 to 2013, we calculate the difference between the initial population (1500 students) and the final population (1485 students) and divide it by the initial population. (1500 - 1485) / 1500 = 15 / 1500 = 0.01 or 1%. Therefore, there was a 1% decrease in the number of students from 2011 to 2013.

Answer 2

-1%

Step-by-step explanation:

The population will not be the same unless the starting value is the same. Percent is a portion of the total 100%. If the total in 2011 and 2012 was different, then the change in population will be different.

• In 2011, the population was 1500 students.
• In 2012, the population was 10% more than 1500. 1500+1500(0.10)=1500+150=1650
• In 2013, the population decreased by 10% from 1650. 1650-1650(0.10)=1650-165=1485.

To find the percent change,

To calculate the percent increase or decrease, we:

• Find the difference between the new value and the original
• Divide the number by the original
• Multiply by 100 and the % symbol.

The population originally in 2011 was 1500. In 12013, the population is 1485.

1485-1500=-15

-15/1500=-0.01

100(-0.01)=-1%

0.75(100)=75%

The towns population increase by 75%