In the image, Jim has kept track of how long it took him to finish his homework each day of the week. The table shows the time spent in minutes for each day, and the question asks for the rate of change between Monday and Wednesday.

Table dataIn the image, Jim has kept track of how long it took him to finish his homework each day of the week. The table shows the time spent in minutes for each day, and the question asks for the rate of change between Monday and Wednesday.

Table

• Monday: 72 minutes
• Tuesday: 73 minutes
• Wednesday: 80 minutes
• Thursday: 78 minutes
• Friday: 72 minutes

Problem:

Find the rate of change between Monday and Wednesday.

The formula for rate of change is: $\text{Rate of change} = \frac{\text{Change in time}}{\text{Change in days}}$

Step 1: Calculate the change in time

$\text{Change in time} = \text{Wednesday's time} - \text{Monday's time} = 80 - 72 = 8 \text{ minutes}$

Step 2: Calculate the change in days

$\text{Change in days} = \text{Wednesday} - \text{Monday} = 2 \text{ days}$

Step 3: Calculate the rate of change

$\text{Rate of change} = \frac{8 \text{ minutes}}{2 \text{ days}} = 4 \text{ minutes per day}$

Thus, the rate of change between Monday and Wednesday is 4 minutes per day.

Would you like more details or have any questions about the solution?

Here are 5 related questions you might consider:

1. What would be the rate of change between Tuesday and Thursday?
2. How could we calculate the total time Jim spent on homework for the whole week?
3. Is the rate of change between any two days always positive? Why or why not?
4. What is the average amount of time Jim spent on homework during the week?
5. How could you graph this data to visualize the rate of change?

Tip: The rate of change formula is commonly used to analyze patterns and trends in data, and it helps in understanding how quickly something is increasing or decreasing over time.