# Lesson 4 Composing and Decomposing Develop Understanding

A school building is kept warm only during school hours, in order to save money. The figure shows a graph of the temperature,

### 1.

In January, many students are sick with the flu. The custodian decides to keep the building

### 2.

If

### 3.

In the spring, the drill team begins early morning practice. The custodian then changes the original setting to start

### 4.

If

In our work, we use the notation

### 5.

Let

#### a.

#### b.

### 6.

Let

#### a.

#### b.

### 7.

Use your answers for parts a and b in problem 6 to calculate the two problems given.

#### a.

#### b.

### 8.

Now use

#### a.

Describe the problem that you encountered when calculating

#### b.

Do you think that the answer you derived in #7 is valid based on what happened in #8? Explain your thinking.

### 9.

Describe the domains of

#### a.

Domain of

#### b.

Domain of

### 10.

What makes the domain for each composition different?

Change each logarithmic expression to an equivalent expression involving an exponent.