The table shows the cost associated with different amounts of minutes, $m$, along with two questions:

Table:

Questions:

• (a) From $m = 500$ to $m = 2,000$
• (b) From $m = 1,000$ to $m = 3,000$

It seems like the question is asking about the rate of change (possibly average rate of change) or the total cost difference over these ranges.

Let's analyze each part:

(a) From $m = 500$ to $m = 2,000$:

• At $m = 500$, the cost is $26$.
• At $m = 2,000$, the cost is $62$.

To calculate the average rate of change (or the slope) between these two points: $\text{Average rate of change} = \frac{\Delta \text{Cost}}{\Delta m} = \frac{62 - 26}{2,000 - 500} = \frac{36}{1,500} = 0.024$ The average rate of change is $0.024 per minute.

(b) From $m = 1,000$ to $m = 3,000$:

• At $m = 1,000$, the cost is $38$.
• At $m = 3,000$, the cost is $86$.

The average rate of change here is: $\text{Average rate of change} = \frac{86 - 38}{3,000 - 1,000} = \frac{48}{2,000} = 0.024$ Again, the average rate of change is $0.024 per minute.

Both parts (a) and (b) give the same average rate of change, which suggests a constant rate of increase in cost over time.

Would you like more details or have any questions?

Related Questions:

1. How do you calculate the total cost increase over a given range of minutes?
2. How can the rate of change help predict future costs?
3. Can you find the cost at $m = 4,000$ using the rate of change?
4. Is this linear relationship applicable for values of $m$ beyond 3,000 minutes?
5. What would the total cost be if the cost per minute was $\$0.03$ instead of $\$0.024$?

Tip:

The average rate of change is a helpful tool for finding trends in data over an interval, especially for linear relationships like this one!