how do you find the rate of change and explain what it means for thhe situation?

heres the table:
Time(hours) Distance(miles)
4 260
6 390
8 520
10 650

Before the hour table started it may have traveled 260 miles in four hours. It is hard to say because no data is given for zero hours. However assuming it was moving from 0 distance to 260 miles in those initial four hours it went 260 miles / 4 hours or 65 miles per hour on the average before he first point in your table.

In the first two hours (from 4 to 6) it went 130 miles or 65 miles per hour
In the second two hours (from 6 to 8) it went 130 miles or 65 miles per hour
In the third two hours (from 8 to 10) it went 130 miles or 65 miles per hour

So the rate of change of distance with time (the speed) is 65 miles per hour over every two hour time interval measured.

To find the rate of change in this scenario, we can use the formula:

Rate of change = (Change in distances) / (Change in time)

Let's calculate the rate of change using the given table:

Change in distances = Final distance - Initial distance
Change in time = Final time - Initial time

Initial distance = 260 miles (at 4 hours)
Final distance = 650 miles (at 10 hours)
Initial time = 4 hours
Final time = 10 hours

Change in distances = 650 miles - 260 miles = 390 miles
Change in time = 10 hours - 4 hours = 6 hours

Rate of change = 390 miles / 6 hours

The rate of change is approximately 65 miles per hour.

This means that the distance is changing by an average of 65 miles for every hour that passes. It represents how the distance traveled (in miles) is changing with respect to time (in hours). In this scenario, the rate of change tells us how fast or slow the object is moving.