To complete the task about China's population growth, follow these steps based on the instructions provided:

Step 1: Research Topic

Since you have chosen the population growth of China, this fits well into an exponential model due to the nature of population increase, especially over large timescales.

Step 2: Introduction and Explanation

You will need to write a brief introduction that answers the following questions:

1. Why did you choose this topic?

   • China has one of the most significant population growth rates in the world, and analyzing its trends can help understand broader implications for economics, resources, and policy-making.

2. Why do you think this topic can be modeled using an exponential model?

   • Population growth is often exponential because each year's growth is compounded by the size of the previous year's population. Exponential models are suitable when growth rates affect the population proportionally.

3. What do you hope to learn by researching this topic?

   • By researching China's population growth, I hope to understand the patterns of increase, predict future population sizes, and evaluate the potential socio-economic impacts of population changes.

Step 3: Data Collection

You will need to collect 6-10 data points on China's population for various years. Here’s a brief guide:

• Use data from reliable sources such as the World Bank or China's national statistics.
• Make sure the data is unique, not copied from any class examples.

For example, you could use the population figures from:

• 1950
• 1960
• 1970
• 1980
• 1990
• 2000
• 2010
• 2020

Step 4: Modeling the Data

Once you have the data, you can create a model:

1. If you're using a linear model, the equation will be of the form: $y = mx + b$ where $y$ represents the population, $x$ the year, $m$ the slope, and $b$ the y-intercept.

2. For an exponential model, the equation would be: $y = a \cdot e^{bx}$ where $y$ is the population, $x$ is the year, $a$ is the initial value, and $b$ is the growth rate.

Clearly define what each variable represents:

• $x$ = Year
• $y$ = Population

Step 5: Ask Questions

From the options provided in the second image, you need to ask two questions related to your model, such as:

1. Interpret the slope (if using a linear model) or interpret the percent growth (for an exponential model).
2. Solve for y given a certain value of x and interpret what the population would be at that time.

Step 6: Provide a Solution

Solve the two questions posed above by using the data and models you developed.

Step 7: Discussion

Finally, explain why your data may or may not follow the model forever. For example, due to policies like the one-child policy or recent demographic trends, China’s population growth may not always be exponential.

Next Steps:

1. Do you need help gathering population data for China?
2. Would you prefer a linear or exponential model for your project?
3. Should I help with the equations or regression on your calculator?
4. Would you like guidance on how to format your sources (MLA or APA)?
5. Should I assist with solving specific questions from Step 5?

Tip:

When working with exponential models, always check the growth rate carefully, as small changes can lead to significant differences over long periods.