today in algebra… learning target : 8.5 you will write and graph exponential growth models. ...

TODAY IN ALGEBRA…

Learning Target : 8.5 You will write and graph exponential growth models.

Independent Practice

8.5 EXPONENTIAL GROWTH FUNCTIONSEXPONENTIAL FUNCTIONS GENERAL FORM:

EXAMPLE: Write a rule for the function.

x -2 -1 0 1 2y 2 6 18

+1+1+1+1

×3×3×3×3

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.

𝟑𝑥2 ∙

8.5 EXPONENTIAL GROWTH FUNCTIONSEXPONENTIAL FUNCTIONS GENERAL FORM:

EXAMPLE2: Write a rule for the function.

x -2 -1 0 1 2y 8 16 32

+1+1+1+1

×2×2×2×2

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.

𝟐𝑥8 ∙

8.5 EXPONENTIAL GROWTH FUNCTIONSEXPONENTIAL FUNCTIONS GENERAL FORM:

PRACTICE: Write a rule for the function.

x -2 -1 0 1 2y 27 81 243

+1+1+1+1

×3×3×3×3

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.

𝟑𝑥27 ∙

8.5 EXPONENTIAL GROWTH 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.

8.5 EXPONENTIAL GROWTH FUNCTIONSPRACTICE: 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.

8.5 EXPONENTIAL GROWTH FUNCTIONSEXAMPLE: Compare the graphs of the functions

.

𝑦=2𝑥𝑦=5𝑥 The graph of grows at a faster rate than the graph of .

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

1. Make a table.

2. Graph the points.

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

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

1. Make a table.

2. Graph the points.

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

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

Initial amountGrowth rate

Time periodGrowth factor

8.5 EXPONENTIAL GROWTH FUNCTIONSEXAMPLE: The owner of a 1953 Hudson Hornet convertible sold the car at an auction. The owner bought it in 1984 when its value was $11,000. The value of the car increased at a rate of 6.9% per year.a. Write a function that models the value of the car over time.

b. The auction took place in 2004. What was the approximate value of the car at the time of the auction?

After 20 years the value of the car is $41,777.92

*Must write the rate as a decimal!

t=After 20 years

8.5 EXPONENTIAL GROWTH FUNCTIONSCOMPOUND INTEREST: You put $250 in a savings account that earns 4% annual interest compounded yearly. You do not make any deposits or withdrawals. How much will your investment be worth in 5 years?

Write a model (equation)

Substitute t=5

Simplify

Use a calculator

In 5 years your investment grew about .

*Must write the rate as a decimal!

HOMEWORK #4:

Pg. 523: 3-7, 10, 14, 18, 22, 24, 28, 30, 38-40

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 Notation