WARM UP 4 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙ 15x when x = – x/3 when x = 9

WARM UP 3 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙ 15x when x = – x/3 when x = 9

WARM UP 2 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙ 15x when x = – x/3 when x = 9

WARM UP 1 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙ 15x when x = – x/3 when x = 9

WARM UP 0 VARIABLE EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 1.3) x 2 When x = 5 2.6x – 1 when x = ∙ 15x when x = – 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 r are positive. The expression (1 + r) is called the growth factor.

8.6 Exponential Growth Functions EXAMPLE 1 W rite an Exponential Growth Model CATFISH GROWTH A newly hatched channel catfish typically weighs about 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.

EXAMPLE 1 W rite 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 The growth rate is r is 10%, or y= C(1 + r) t = 0.006( ) 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.

EXAMPLE 2 F ind 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?

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( ) 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?