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WARM UP. 4. VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) 24 + x 2 When x = 5 6x – 1 when x = 1 3 ∙ 15x when x = 2 1 – x/3 when x = 9. WARM UP. 3.

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WARM UP

4

VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

24 + x2 When x = 5

6x – 1 when x = 1

3 ∙ 15x when x = 2

1 – x/3 when x = 9

WARM UP

3

VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

24 + x2 When x = 5

6x – 1 when x = 1

3 ∙ 15x when x = 2

1 – x/3 when x = 9

WARM UP

2

VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

24 + x2 When x = 5

6x – 1 when x = 1

3 ∙ 15x when x = 2

1 – x/3 when x = 9

WARM UP

1

VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

24 + x2 When x = 5

6x – 1 when x = 1

3 ∙ 15x when x = 2

1 – x/3 when x = 9

WARM UP

0

VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

24 + x2 When x = 5

6x – 1 when x = 1

3 ∙ 15x when x = 2

1 – x/3 when x = 9

### 8.6 Exponential Growth Functions

GOAL

Write exponential growth functions.

KEY WORDS

Exponential growth

Growth rate

Growth factor

### 8.6 Exponential Growth Functions

EXONENTIAL GROWTH

A quantity is growing exponentially if it increases by the same percent r in each unit of time t. This is called exponential growth. Exponential growth can be modeled by the equation

y = C(1 + r)t

### 8.6 Exponential Growth Functions

EXONENTIAL GROWTH

y = C(1 + r)t

C is the initial amount (the amount before any growth occurs), r is the growth rate (as a decimal), t represents time, and both C and rare positive.

The expression (1 + r) is called the growth factor.

### 8.6 Exponential Growth Functions

EXAMPLE 1 Write an Exponential Growth Model

CATFISH GROWTH A newly hatched channel catfish typically weighs about 0.006 gram. During the first six weeks of life, its weight increases by about 10% each day. Write a model for the weight of the catfish during the first six weeks.

### 8.6 Exponential Growth Functions

EXAMPLE 1 Write an Exponential Growth Model

SOLUTION

Let y be the weight of the catfish during the first six weeks and let t be the number of days. The initial weight of the catfish C is 0.06. The growth rate is r is 10%, or 0.10.

y= C(1 + r)t

= 0.006(1 + 0.10)t

= 0.006(1.1)t

### 8.5 Scientific Notation

Checkpoint Write an Exponential Growth Model

1. A TV station’s local news program has 50,000 viewers. The managers of the station hope to increase the number of viewers by 2% per month. Write an exponential growth model to represent the number of viewers v in t months.

### 8.6 Exponential Growth Functions

COMPOUND INTEREST

Compound interest is interest paid on the principal P, the original amount deposited, and on the interest that has already been earned. Compound interest is a type of exponential growth, so you can use the exponential growth model to find the account balance A.

### 8.6 Exponential Growth Functions

EXAMPLE 2Find the Balance in an Account

COMPOUND INTEREST

You deposit \$500 in an account that pays %8 interest compounded yearly. What will the account balance be after 6 years?

### 8.6 Exponential Growth Functions

EXAMPLE 1 Write an Exponential Growth Model

SOLUTION

The initial amount P is \$500, the growth rate is %8, and the time is 6 years.

A = P(1 + r)t

= 500(1 + 0.08)t

= 500(1.08)t

= 793

### 8.5 Scientific Notation

Checkpoint Write an Exponential Growth Model

2. You deposit \$750 in an account that pays 6% interest compounded yearly. What is the balance in the account after 10 years?