WARM UP 4VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

1. 24 + x2 When x = 5

2. 6x – 1 when x = 1

3. 3 15x when x = 2∙

4. 1 – x/3 when x = 9

WARM UP 3VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

1. 24 + x2 When x = 5

2. 6x – 1 when x = 1

3. 3 15x when x = 2∙

4. 1 – x/3 when x = 9

WARM UP 2VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

1. 24 + x2 When x = 5

2. 6x – 1 when x = 1

3. 3 15x when x = 2∙

4. 1 – x/3 when x = 9

WARM UP 1VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

1. 24 + x2 When x = 5

2. 6x – 1 when x = 1

3. 3 15x when x = 2∙

4. 1 – x/3 when x = 9

WARM UP 0VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3)

1. 24 + x2 When x = 5

2. 6x – 1 when x = 1

3. 3 15x when x = 2∙

4. 1 – x/3 when x = 9

8.6 Exponential Growth Functions

GOALWrite exponential growth functions.KEY WORDS• Exponential growth• Growth rate• Growth factor

8.6 Exponential Growth Functions

EXONENTIAL GROWTHA 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 GROWTHy = 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 r are positive. The expression (1 + r) is called the growth factor.

8.6 Exponential Growth Functions

EXAMPLE 1 Write an Exponential Growth ModelCATFISH 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 ModelSOLUTIONLet 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 Model1. 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 INTERESTCompound 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 2 Find the Balance in an AccountCOMPOUND 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 ModelSOLUTIONThe 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 Model2. You deposit $750 in an account that pays 6% interest compounded yearly. What is the balance in the account after 10 years?