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In this lesson, students explore exponential models in context. The teacher leads students through a series of questions that show that there are multiple ways to analyze data and build models. Students compare the exponential functions and methods from data in a previous lesson. Then, the class learns to linearize data as an important tool in developing mathematical models for data.

In this lesson, students learn to:

• Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions.
• Generalize patterns using explicitly defined and recursively defined functions.
• Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
• Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts.
• Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.
• Draw reasonable conclusions about a situation being modeled.

North Carolina Curriculum Alignment