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.

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.