Question

the following table gives the population in a small coastal community for the period 2002 - 2020. figures shown are for january 1 each year.
(a) what was the average rate of change of population (in persons/yr) between 2004 and 2012?
persons/yr
(b) what was the average rate of change of population (in persons/yr) between 2012 and 2020?
persons/yr
(c) for what period of time was the population increasing?
2008 - 2020
2010 - 2020
2002 - 2012
2012 - 2020
2014 - 2018
(d) for what period of time was the population decreasing?
2004 - 2010
2008 - 2014
2002 - 2020
2012 - 2020
2002 - 2012

Explanation:

Step1: Calculate the average rate of change formula

The formula for the average rate of change is $\frac{\Delta y}{\Delta x}=\frac{y_2 - y_1}{x_2 - x_1}$, where $y$ represents population and $x$ represents year.

Step2: Solve part (a)

For 2004 - 2012: $x_1 = 2004$, $y_1=3645$, $x_2 = 2012$, $y_2 = 6375$.
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{6375 - 3645}{2012 - 2004}=\frac{2730}{8}=341.25$

Step3: Solve part (b)

For 2012 - 2020: $x_1 = 2012$, $y_1 = 6375$, $x_2=2020$, $y_2 = 4636$.
$\frac{y_2 - y_1}{x_2 - x_1}=\frac{4636 - 6375}{2020 - 2012}=\frac{- 1739}{8}=-217.375$

Step4: Solve part (c)

Check the population trend:

• 2002: 3220
• 2004: 3645
• 2006: 4357
• 2008: 4869
• 2010: 5871
• 2012: 6375
• 2014: 6288
• 2016: 5318
• 2018: 4921
• 2020: 4636

The population is increasing from 2002 - 2012.

Step5: Solve part (d)

Check the population trend:
From 2012 - 2020, the population values are 6375 (2012), 6288 (2014), 5318 (2016), 4921 (2018), 4636 (2020). So it is decreasing from 2012 - 2020.

Answer:

a. $341.25$ persons/yr
b. $- 217.375$ persons/yr
c. 2002 - 2012
d. 2012 - 2020