# Lesson 6 Compounding the Problem Develop Understanding

Use first and second differences to identify the pattern in each table as linear, quadratic, or neither. If the pattern is linear, write both the explicit and recursive equations. If the pattern is quadratic, write only the recursive equation. If the pattern is neither, identify it as neither and stop.

### 1.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

### 2.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

### 3.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

### 4.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

### 5.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

### 6.

#### a.

Identify the pattern in the table as linear, quadratic, or neither.

#### A.

linear

#### B.

quadratic

#### C.

neither

#### b.

If the pattern is linear, what is the explicit equation?

#### c.

If the pattern is linear or quadratic, what is the recursive equation?

Recall the equations for compound interest you used in class today:

### 7.

A

### 8.

How much will the investment earn if it is compounded continuously at the same interest rate for

### 9.

Fill in the table for each of the given functions. Then graph each function on the same axes.

#### a.

#### b.

#### c.

#### d.

Graph each function on the same axes.

### 10.

What point do all three functions from problem 9 share? Why?

### 11.

Given that

#### a.

#### b.

#### c.

Write an expression that describes the relationship between

Fill in the blanks.

### 12.

### 13.

### 14.

Given

### 15.

### 16.

Given

### 17.

If