Alg 1 Unit 2 overview

Alg 1 Unit 2 overview

Linear vs Exponential

Pros/Cons of Linear

• Stays constant throughout

• At the beginning, starts out with more (think about Avi and Benita money)

• It will never increase the amount it is going up by

Pros/Cons of Exponential

• Increases by more and more each time

• Ends (takes a while) growing way faster than linear

• Starts out very slow (most of the time)

Poll

If you had the option to choose between a bank account that increases by a constant amount or a bank account that grows by a percent, which would you choose?

• Grows by constant amount

• Grows by a percent

• It depends... / I'm not sure

Multiple Select

Select all that are true about linear functions

• They grow by a multiplier

• They grow by a constant rate of change

• Arithemetic sequences are types of linear functions

• Their graph is curved

• Their equation looks like y=b(g)^x

Multiple Select

Select all of the following representations that show an exponential pattern

• 4, 8, 16, 32...

• y = 7 + 2x

• y = 7(2)^x

All Sequences...

• Use t(n)= for their equation notation to communicate that they are a sequence

• Have a domain of positive whole numbers (inputs)

• Are a list of numbers that follow a pattern

• The two types of sequences we talked about were arithmetic and geometric (arithmetic = adding)(geometric = multiplying)

Arithmetic Sequences

• 5, 7, 9, 11

• 100, 95, 90, 85...

• 3.5, 4.5, 5.5, 6.5...

• -1, -7, -13, -19...

Geometric Sequences

• 1, 3, 9, 27...

• 400, 200, 100, 50, 25....

• 6, 9, 13.5, 20.25

• 300, 315, 330.75, 347.2875

Multiple Choice

What is the equation for the following sequence: 3, 8, 13, 18...

• t(n) = 3 +5n

• t(n) = 3(5)ⁿ

• t(n) = -2 +5n

• t(n) = n+5

Multiple Choice

What is the equation for the following sequence: 10, 50, 250, 1250...

• t(n) = 10 +5n

• t(n) = 2(5)ⁿ

• t(n) = -n * 10

• t(n) = 10 * 5ⁿ

Exponential Equations (using percent increase/decrease)

• Remember that you always start with 100%

• Increase by 5% every month results in a multiplier of 1.05

• I started with 400 and my account gets an interest rate of 2% every year. y = 400(1.02)^x

Multiple Choice

Choose the equation for: "Dawson started with $300 and he gets 3% interest every year."

• y = 300(1.03)^x

• y = 300(0.03)^x

• y = 300 + 1.03x

• y = 300 (3)^x

Multiple Choice

Given the equation y = 1000(1.25)^x choose the correct situation

• Natalie started with $1000 and increases by 1.25%

• Natalie started with $1000 and increases by 25%

• Natalie started with $1.25and increases by 1000%

• Natalie started with $1000 and increases by 1.25%

Multiple Choice

Which equation would be decreasing?

• y = .50(2)^x

• y = 1000(1.02)^x

• y = 200(1.10)^x

• y = 400(.98)^x

Linear, exponential, arithmetic, geometric

• Linear and arithmetic have a pattern of a constant rate of change

• Exponential and geometric have a pattern of a constant multiplier

• Linear and exponential FUNCTIONS can have any domain (include negatives and decimals/fractions), their graph is a solid line

• Arithmetic and Geometric SEQUENCES can only have a domain of POSITIVE WHOLE NUMBERS and their graphs will be dotted

Multiple Choice

Miss Mahoney started with 100 pencils and loses 5 throughout every day. Is this a linear, exponential, arithmetic or geometric...

• Linear function

• Exponential function

• Arithmetic Sequence

• Geometric Sequence

Multiple Choice

The height of a bouncy ball after having bounced a certain number of times. Which category does this BEST fit into?

• Linear function

• Exponential function

• Arithmetic Sequence

• Geometric Sequence