**Part b: Identify the correct graph**

You calculated the **average rate of change** for each period as follows:

**1850**: 5.6

**1900**: 7.8

**1950**: 17.4

**2000**: 71.2

**2050**: 64.74 2000 and 2050 are both wrong

It looks like you are working with data related to the **average rate of change** over different periods, but there might be errors in the calculations for **2000** and **2050**. Let's go through the steps for finding the **correct values**.

### How to Calculate the Average Rate of Change

The **average rate of change** of a function between two points is given by the formula:

\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]

Where:
- \( f(b) \) is the function value at the end of the period.
- \( f(a) \) is the function value at the beginning of the period.
- \( b \) and \( a \) are the years marking the period's end and start.

### To Proceed:
1. Could you provide the specific **data values** for the years 2000 and 2050 (like population or other dependent values)?
2. If you have graphs available, please upload them, and I can assist you further by identifying the correct graph.

Let me know if you want a more detailed explanation of how to perform the calculations!

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### 5 Related Questions:
1. How do you interpret the average rate of change in real-life scenarios?
2. What data are you working with in this case (e.g., population, temperature)?
3. How can we use the average rate of change to predict future trends?
4. What role does the average rate of change play in identifying patterns in data?
5. How does this method differ from calculating instantaneous rates of change?

### Tip:
When analyzing trends, always double-check the data points used for the calculation to ensure accuracy.

Discover how to calculate the average rate of change for data points from 1850 to 2050 and identify the correct graph. This guide includes detailed explanations and calculations, focusing on years 2000 and 2050. Ideal for high school students learning about data trends and graph interpretation.

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