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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
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 up1
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 up2
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 up3
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 up4
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

8.6 Exponential Growth Functions

GOAL

Write exponential growth functions.

KEY WORDS

Exponential growth

Growth rate

Growth factor

8 6 exponential growth functions1

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 functions2

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 functions3

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 functions4

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

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 functions5

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 functions6

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 functions7

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 notation1

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?