Question

4. The percent of voters between the ages of 18 and 29 that participated in each United

States presidential election between the years 1988 to 2016 are shown in the table.
year
percentage
of voters
ages 18-29
1988 1992 1996
35.7 42.7
33.1
2000
2004
2008 2012 2016
34.5 45,0 48.4 40.9
The function P gives the percent of voters between 18 and 29 years old that
participated in the election in year 1.
a. Determine the average rate of change for P between 1992 and 2000.
43.4
b. Pick two different values of r so that the function has a negative average rate of
change between the two values. Determine the average rate of change.
c. Pick two values of r so that the function has a positive average rate of change
between the two values. Determine the average rate of change.
(PS: PLEASE do not answer with links to websites or videos, I need an actual answer.)

Answer 1

a. The average rate of change for \( P \) between 1992 and 2000 is calculated as follows:

\[ \text{Average rate of change} = \frac{P(2000) - P(1992)}{2000 - 1992} \]

\[ \text{Average rate of change} = \frac{45.0 - 42.7}{2000 - 1992} \]

\[ \text{Average rate of change} = \frac{2.3}{8} \]

\[ \text{Average rate of change} = 0.2875 \]

So, the average rate of change for \( P \) between 1992 and 2000 is \( 0.2875\% \) per year.

b. Look for two consecutive years where \( P \) decreases. Let's take \( r_1 = 2004 \) and \( r_2 = 2008 \).

\[ \text{Average rate of change} = \frac{P(2008) - P(2004)}{2008 - 2004} \]

\[ \text{Average rate of change} = \frac{48.4 - 45.0}{2008 - 2004} \]

\[ \text{Average rate of change} = \frac{3.4}{4} \]

\[ \text{Average rate of change} = 0.85 \]

So, the average rate of change for \( P \) between 2004 and 2008 is \( 0.85\% \) per year.

c. Look for two consecutive years where \( P \) increases. Let's take \( r_3 = 1996 \) and \( r_4 = 2000 \).

\[ \text{Average rate of change} = \frac{P(2000) - P(1996)}{2000 - 1996} \]

\[ \text{Average rate of change} = \frac{34.5 - 33.1}{2000 - 1996} \]

\[ \text{Average rate of change} = \frac{1.4}{4} \]

\[ \text{Average rate of change} = 0.35 \]

So, the average rate of change for \( P \) between 1996 and 2000 is \( 0.35\% \) per year.