# Lesson 7

Interpreting and Using Exponential Functions

### Lesson Narrative

So far in this unit, students have interpreted, evaluated, and constructed exponential functions in various applications. Here, they encounter exponential functions in a new context—that of radioactive decay. Though the mathematics is not new, students need to apply what they have learned to solve problems that are less straightforward and less scaffolded, which requires sense making and perseverance (MP1).

The idea of radioactive decay is not necessarily intuitive, so answering questions about remaining amounts of radioactive substances and about dates in the distant past calls for considerable quantitative and abstract reasoning (MP2).

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

### Learning Goals

Teacher Facing

• Comprehend the term “half-life” in relation to the radioactive decay of certain elements and use it to calculate the age of different objects.
• Describe (in writing) the parameters of exponential expressions that represent different decay situations.

### Student Facing

• Let’s explore the ages of ancient things.

### Student Facing

• I can use the half-life of elements to calculate how much of the element remains over time.