# Lesson 1 Piggies and Pools Develop Understanding

## Learning Focus

Represent situations with different types of growth.

Compare models for situations that occur over time.

What type of situation can be modeled by a continuous graph? When is a graph of only separate points appropriate?

What are the similarities and differences between an arithmetic sequence and a linear function?

Can a geometric sequence be continuous?

## Open Up the Math: Launch, Explore, Discuss

### 1.

My little sister, Savannah, is three years old. She has a piggy bank that she wants to fill. She started with

Table:

Equations:

### 2.

Our family has a small pool for relaxing in the summer that holds

Equation:

Table:

### 3.

I’m more sophisticated than my little sister, so I save my money in a bank account that pays me

Equation:

Table:

### 4.

At the end of the summer, I decided to drain the

Equation:

Table:

### 5.

Compare problems 1 and 3. What similarities do you see? What differences do you notice?

Similarities:

Differences:

### 6.

Compare problems 1 and 2. What similarities do you see? What differences do you notice?

Similarities:

Differences:

### 7.

Compare problems 3 and 4. What similarities do you see? What differences do you notice?

Similarities:

Differences:

## Ready for More?

Use your model in problem 4 to find when the pool will be empty. Justify your answer.

## Takeaways

A geometric sequence

Exponential functions

Discrete functions

Continuous functions

Arithmetic and geometric sequences are

## Adding Notation, Vocabulary, and Conventions

Domain of a function:

## Vocabulary

- continuous function/discontinuous function
- discrete function
- domain
- exponential function
- linear function
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned that the possible inputs for a function are called the domain. We found that some situations are best described using a discrete model and others are represented better with a continuous model. Arithmetic sequences are part of the linear family of functions and geometric sequences are part of the exponential family of functions.

### 1.

For each sequence, find the next two terms in the sequence and then state whether the sequence is arithmetic, geometric, or neither. Justify your answer.

#### a.

#### b.

#### c.

Find the unit rate for each of the items.

### 2.

A dozen ears of corn for

### 3.

Three t-shirts for

Solve each of the equations.