Question

1. -/2 pointsthe following table shows the past and projected populations of baby boomers for the years 2000, 2031, and 2046. (a) find the average rate of change per year in the population of the baby boomer generation from 2031 to 2046. (note: a negative average rate of change denotes a decrease. round to the nearest hundred thousand.) million people per year(b) find the average rate of change per year in the population of baby boomers from 2000 to 2046. round to the nearest hundred thousand.million people per year

Explanation:

Step1: Recall the formula for average rate of change

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

Step2: Solve part (a)

For the period from 2031 to 2046:

• $y_1 = 51$, $y_2=19$, $x_1 = 2031$, $x_2 = 2046$
• $\Delta y=y_2 - y_1=19 - 51=-32$
• $\Delta x=x_2 - x_1=2046 - 2031 = 15$
• Average rate of change $=\frac{-32}{15}\approx - 2.13$

Step3: Solve part (b)

For the period from 2000 to 2046:

• $y_1 = 79$, $y_2 = 19$, $x_1=2000$, $x_2 = 2046$
• $\Delta y=y_2 - y_1=19 - 79=-60$
• $\Delta x=x_2 - x_1=2046 - 2000=46$
• Average rate of change $=\frac{-60}{46}\approx - 1.30$

Answer:

(a) $-2.13$ million people per year
(b) $-1.30$ million people per year