Overview of Task Model Session: Modeling a Non-Periodic Context

Presenters

• Jamil Sadiki, East Bridgewater Junior/Senior High School, Massachusetts
• Becky Barn, West Springfield High School, Springfield, Virginia

Key Points of Task Model

• Free Response Question No. 2 focuses on modeling a non-periodic context.
• Scored out of 6 points.
• Requires a graphing calculator, always set in radian mode.
• Content from Units 1 and 2.
• Real-world context.
• Function types: Piecewise, exponential, and logarithmic.
• Consists of 3 parts: Constructing a model, working with average rates of change, and justifying conclusions about the model.
• Consideration of the model's limitations.

Part A: Constructing the Model

• Given data: Impact of conservation on species population from 2015-2021.
• Population model: $P(T) = A + B \cdot \ln(T + 1)$
• Part A Objective: Use data to write equations for constants A and B.
• Approach: Set up equations using given data points $T=0$ (230 animals) and $T=6$ (580 animals).

Part B: Average Rate of Change

• Objective: Find average rate of change and interpret in context.
• Calculation: Use population data at $T=0$ and $T=6$.
• Interpretation: On average, the population increases by 58.33 animals per year.

Part C: Domain Limitations and Conclusion

• Objective: Consider maximum sustainable population (800 animals) to determine domain limitations.
• Analyze where the population model predicts reaching 800 animals using graphing technology.
• Result: Domain for the function is 0 to approximately 22.785 years post-2015, rounded to 22.78 for simplicity.

Teaching Points

• Importance of clear notation and presentation during exams.
• Utilizing technology effectively in solving and interpreting mathematical problems.
• Understanding the practical application of mathematical models in real-world contexts, including their limitations and assumptions.