TODAY IN ALGEBRA…Warm up: Sequences

Learning Target 1: 8.6 You will write and graph exponential decay functions.

Learning Target 2: You will use what you understand about exponential functions to find geometric sequences

Independent Practice/HW #4 Due Today

CH. 8 TEST FRIDAY!

WARM UP: Complete the Arithmetic and Geometric sequences half sheet. We will go over the solutions as a class.

ARITHMETIC SEQUENCES:ADDING a positive or negative constant.

EX. Find the 8th term of the sequence:1 3 42

−10−10−10

5 7 86

GEOMETRIC SEQUENCES:MULTIPLYING a positive or negative constant.

EX. Find the 8th term of the sequence:1 3 42

×−3

5 7 86

×−3×−3

8.6 EXPONENTIAL DECAY FUNCTIONSEXPONENTIAL FUNCTIONS GENERAL FORM:

EXAMPLE: Write a rule for the function.

x -2 -1 0 1 2y

+1+1+1+1

×14×14×14×14

Check to make sure that the x’s are increasing by 1.

Find what number the previous term is MULTIPLIED by to get the next term. This will be b in your equation.Find the value for y when .

This will be a in your equation.

1 ∙

8.6 EXPONENTIAL DECAY FUNCTIONSEXPONENTIAL FUNCTIONS GENERAL FORM:

EXAMPLE: Write a rule for the function.

x -2 -1 0 1 2y

+1+1+1+1

×15×15×15×15

Check to make sure that the x’s are increasing by 1.

Find what number the previous term is MULTIPLIED by to get the next term. This will be b in your equation.Find the value for y when .

This will be a in your equation.

1 ∙

8.6 EXPONENTIAL DECAY FUNCTIONSEXAMPLE: Graph the function . Identify the domain and range.

1. Make a table.

2. Graph the points.

Domain: All real numbersRange: All numbers greater than zero.

8.6 EXPONENTIAL DECAY FUNCTIONSEXAMPLE: Graph the function . Identify the domain and range.

1. Make a table.

2. Graph the points.

Domain: All real numbersRange: All numbers greater than zero.

8.6 EXPONENTIAL DECAY FUNCTIONSEXAMPLE: Compare the graphs of the functions

.

The graph of decreases at a faster rate than the graph of .

8.5 EXPONENTIAL GROWTH FUNCTIONSEXAMPLE: Graph the functions and . Compare each graph with the graph of .

is a vertical stretch of 3 of . is a vertical shrink and reflection of .

8.6 EXPONENTIAL DECAY FUNCTIONSEXPONENTIAL DECAY MODEL: to find an amount to which a quantity grows after time t.

Initial amountDecay rate

Time periodDecay factor

8.5 EXPONENTIAL GROWTH FUNCTIONSEXAMPLE: The number of acres of Ponderosa pine forests decreased in the western US from 1963 to 2002 by 0.5% annually. In 1963 there were about 41 million acres of Ponderosa pine forests.a. Write a function that models number of pine forests over time.

b. How many million acres of forest were there in 2002?

After 39 years there were about 33.7 million acres of pine forests.

*Must write the rate as a decimal!

t=After 39 years

In millions

8.5 EXPONENTIAL GROWTH FUNCTIONSCOMPOUND INTEREST: A farmer bought a tractor in 1999 for $30,000. The value of the tractor has been decreasing at a rate of 18% per year. What was the approximate value of the tractor in 2005?

Write a model (equation)

Substitute t=6

Simplify

Use a calculator

In 6 years the value of the tractor dropped $20,880!

*Must write the rate as a decimal!

HOMEWORK #5:

Pg. 535: 3-6, 10, 14, 20, 24, 28, 32-34, 47-49

If finished, work on other assignments:

HW #1: Pg. 492: 4-48 evenHW #2: Pg. 498: 4-44 evenHW #3: Pg. 506: 4-44 evenIn Class Work: Scientific NotationHW #4: 523: 3-7, 10, 14, 18, 22, 24, 28, 30, 38-40