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In the provided image, you need to identify the appropriate growth model for each scenario based on how each quantity is changing. Let's analyze each one:

1. **The number of new polio cases has been cut in half each year due to vaccination efforts.**
   - Since the number of cases is being halved annually, this represents a **decreasing exponential (geometric decay) model**. Halving is an example of exponential decay, as the quantity reduces by a fixed percentage each year.

2. **The number of arrests grew for several years, but now has been decreasing.**
   - This suggests a **decreasing trend** (not strictly exponential). Since it mentions "grew for several years" and "now decreasing," it might not strictly follow an exponential model and could represent a more complex trend that doesn’t fit an exponential form. However, if forced to choose, "decreasing" aligns with exponential decay if a decay model is intended.

3. **Tuition is currently $2,000 a quarter and has been growing by 7% a year.**
   - This is a **growth model** with a fixed percentage increase, which is **exponential growth**. A consistent percentage increase, like 7% annually, is characteristic of exponential (geometric) growth.

4. **The amount of pollutants in the lake has been increasing by 4 milligrams per liter each year.**
   - This represents a **linear growth** model, as the increase is by a constant amount (4 milligrams per liter each year), not a percentage. This would not be exponential, as exponential growth requires a percentage or rate-based increase rather than a fixed amount.

Let me know if you would like additional details or have further questions.

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Here are some related questions for practice:

1. How can we distinguish between linear and exponential growth?
2. What real-world scenarios would typically involve exponential decay?
3. How does a growth rate in percentage differ from a constant addition in quantity?
4. Why is a constant halving each year considered exponential decay?
5. How would the growth model change if tuition increased by $200 per year instead of 7%?

**Tip:** Exponential growth/decay typically involves multiplying by a consistent percentage or fraction, whereas linear change involves adding or subtracting a fixed amount.

For each scenario, identify the appropriate growth model that describes how it's changing.

Explore how to identify growth models for real-world scenarios, including exponential growth, exponential decay, and linear growth. This problem involves analyzing various cases to determine the appropriate mathematical model for changes in polio cases, arrests, tuition fees, and pollution levels.

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