The image shows four scenarios where different growth models (either "Exponential" or "Linear") are applied to describe the changes in various quantities. Here's an analysis of each case:

1. Pollutants in the lake: "The amount of pollutants in the lake has been increasing by 4 milligrams per liter each year."

   • This represents a constant increase (by the same amount each year), which indicates linear growth. The selection of "Exponential" is incorrect here. The correct model is Linear.

2. Number of arrests: "The number of arrests grew for several years but now has been decreasing."

   • Since the number of arrests has been growing but has now been decreasing (likely at a constant rate over time), this is best modeled as Linear. The "Linear" choice is correct.

3. Polio cases: "The number of new polio cases has been cut in half each year due to vaccination efforts."

   • Cutting in half every year is a clear indicator of exponential decay, as the reduction is proportional to the current amount. The selection of "Exponential" is correct.

4. Tuition increase: "Tuition is currently $2,000 a quarter and has been growing by 7% a year."

   • A growth by a percentage per year implies exponential growth, as the increase is proportional to the current value. The selection of "Linear" here is incorrect; it should be Exponential.

Let me know if you'd like further clarification or more details.

Here are 5 questions related to these topics:

1. How can we distinguish between linear and exponential models based on data trends?
2. What are some real-world applications of exponential decay other than vaccination efforts?
3. How would the growth model change if tuition increased by a fixed dollar amount each year instead of a percentage?
4. Why is exponential growth often more impactful in long-term financial contexts?
5. What mathematical equation would represent the growth of tuition under the exponential model?

Tip: Linear growth adds a constant value, while exponential growth multiplies by a constant percentage or ratio.