Let's go through the problem step-by-step based on what we see in the image.

Part b: Calculating the Rate of Change

To find the rate of change, we'll use the two ordered pairs given in the table:

• Point 1: $(3, 63525)$
• Point 2: $(5, 86731)$

The rate of change (or slope) is calculated as follows: $\text{Rate of Change} = \frac{\Delta O}{\Delta I} = \frac{86731 - 63525}{5 - 3}$

Calculating this:

1. $86731 - 63525 = 23206$
2. $5 - 3 = 2$

So, $\text{Rate of Change} = \frac{23206}{2} = 11603$

Therefore, the rate of change is 11,603 vehicles per year.

Part c: Filling in Missing Values Using the Rate of Change

Work for Year 0:

We need to use the rate of change to determine the number of all-electric vehicles for year 0.

1. Since we're going backward from year 3 to year 0, we have $\Delta I = -3$.
2. Using the rate of change we calculated: $\Delta O = \Delta I \times (\text{Rate of Change}) = -3 \times 11603 = -34809$
3. The number of vehicles at year 3 is 63,525. So, for year 0: $63525 + (-34809) = 28716$

Thus, the estimated number of all-electric vehicles in year 0 is 28,716.

Work for 104,492:

Now, we are asked to find the year associated with 104,492 all-electric vehicles.

1. The value at year 5 is 86,731, so $\Delta O = 104492 - 86731 = 17761$.
2. Using the rate of change again, we find $\Delta I$ by dividing: $\Delta I = \frac{17761}{11603} \approx 1.53$
3. Adding this $\Delta I$ to year 5: $5 + 1.53 \approx 6.53$

So, 104,492 all-electric vehicles would likely correspond to around 6.53 years since 2011, which is around mid-2017.

Would you like further details on each step? Here are some follow-up questions to deepen understanding:

1. How is the rate of change used to make predictions?
2. What are other methods to calculate the rate of change for nonlinear data?
3. How can you interpret the negative and positive signs in the rate of change calculations?
4. How would this rate of change affect future predictions if extended to more years?
5. What could cause deviations from this linear rate of increase in real-world data?

Tip: When working with rates of change, it's useful to understand them as slopes of lines connecting two points on a graph, which helps visualize the trend in data.