# Lesson 3

Representing Exponential Growth

### Lesson Narrative

In this lesson, students study a situation characterized by exponential change and learn the term growth factor. They represent this relationship using a table, an expression, and a graph. They also explain the meaning of the numbers $$a$$ and $$b$$ in an exponential expression $$a \boldcdot b^x$$, identifying their meaning in terms of a context ($$a$$ is the initial amount and $$b$$ is the multiplier or growth factor) and also in terms of a graph (where $$a$$ is the vertical intercept and $$b$$ determines how quickly the graph increases). Students interpret the different representations of growth in terms of a bacteria population (MP2).

In this and following lessons, students will often work with properties of exponents, a topic developed in grade 8. There is an optional activity intended to remind students of the convention that $$a^0 = 1$$ for a non-zero number $$a$$.

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

• Explain (in writing) how to see $a$ and $b$ on the graph of an equation of the form $y=a \boldcdot b^x$.
• Interpret $a$ and $b$ given equations of the form $y=a \boldcdot b^x$ and a context of exponential growth.
• Write an equation of the form of $y =a \boldcdot b^x$ to represent a quantity $a$ that changes by a growth factor $b$.

### Student Facing

Let’s explore exponential growth.

### Required Preparation

Acquire devices that can run Desmos (recommended) or other graphing technology as an optional tool for students.

### Student Facing

• I can explain the connections between an equation and a graph that represents exponential growth.
• I can write and interpret an equation that represents exponential growth.

Building On

Building Towards

### Glossary Entries

• growth factor

In an exponential function, the output is multiplied by the same factor every time the input increases by one. The multiplier is called the growth factor.

### Print Formatted Materials

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