Question

• / 4 points

the following table shows the projected population of adults 18 to 19 years old for selected years from 2005 to 2030.
(a) find the average annual rate of change of the u.s. population of adults 18 - 19 years old from 2010 to 2025. adults ages 18 - 19 per year
(b) in which five - year period shown did the average annual rate of change of this population decline?
what was the average annual rate of change for that period? adults ages 18 - 19 per year
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Explanation:

Step1: Calculate the average annual rate of change for part (a)

The formula for the average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$. Here, $y_1 = 8.6$ (population in 2010), $y_2=9.0$ (population in 2025), $x_1 = 2010$, $x_2 = 2025$.
$\frac{9.0 - 8.6}{2025 - 2010}=\frac{0.4}{15}\approx0.0267$

Step2: Analyze each five - year period for part (b)

• 2005 - 2010: $\frac{8.6 - 8.4}{2010 - 2005}=\frac{0.2}{5}=0.04$
• 2010 - 2015: $\frac{8.1 - 8.6}{2015 - 2010}=\frac{- 0.5}{5}=-0.1$
• 2015 - 2020: $\frac{8.6 - 8.1}{2020 - 2015}=\frac{0.5}{5}=0.1$
• 2020 - 2025: $\frac{9.0 - 8.6}{2025 - 2020}=\frac{0.4}{5}=0.08$
• 2025 - 2030: $\frac{9.4 - 9.0}{2030 - 2025}=\frac{0.4}{5}=0.08$

Answer:

a. Approximately $0.0267$ million adults ages 18 - 19 per year.
b. The five - year period is 2010 - 2015. The average annual rate of change is $- 0.1$ million adults ages 18 - 19 per year.