Question

pick two different values of t so that the function has a negative average rate of change between the two values. determine the average rate of change

Answer 1

1. The average rate of change for P from 1992 to 2000 is -1.025.

2. At t = 1996 and t = 1992, the function exhibits a negative average rate of change, with a value of -2.4.

3. At t = 2000 and t = 1996, the function shows a positive average rate of change, with a value of 0.35.

1. To determine the average rate of change between 1992 and 2000 in voter percentages (42.7%, 33.1%, and 34.5%), we use the formula:

`\[ \text{Average Rate} = \frac{\text{Change in Percentage}}{\text{Change in Years}} \]`

The rate of change between 1992 and 1996 (R₁) is calculated as:

`\[ R₁ = (33.1 - 42.7)/(1996 - 1992) = -2.4 \]`

The rate of change between 1996 and 2000 (R₂) is calculated as:

`\[ R₂ = (34.5 - 33.1)/(2000 - 1996) = 0.35 \]`

The average rate of change is given by:

`\[ \text{Average Rate} = (R₁ + R₂)/(2) = (-2.4 + 0.35)/(2) = -1.025 \]`

2. One pair of values (1996 and 1992) where the rate of change is negative is calculated as:

`\[ R = (33.1 - 42.7)/(1996 - 1992) = -2.4 \]`

3. One pair of values (1996 and 2000) where the rate of change is positive is calculated as:

`\[ R = (34.5 - 33.1)/(2000 - 1996) = 0.35 \]`

In summary, the average rate of change between 1992 and 2000 is -1.025. The rate is negative between 1996 and 1992 and positive between 1996 and 2000.