Linear vs. Exponential Functions

Linear Exponential Equation

Table

A constant difference of: ______________

A constant multiplier of: ________________

Key words

Graph

Word Problems

Linear Exponential

Farmer Farah bought a barn containing 350 bales of hay. Each day, she stacks 30 more bales of hay in the barn. Let H be the number of bales of hay in the barn after t days.

75 people reach the summit of Mount Everest every year. In 1996, there were 530 people who had reached the summit. Let P be the number people who have reached the summit, and y be the number of years since 1996.

The number of visitors to the Eiffel Tower in paris increases by 1.5% each year. In the year 2000, 100,000 people visited the Eiffel Tower. Let v be the number of visitors to the Eiffel Tower, and y be the number of years since 2000.

The number of people creating cat videos decreases by 16% every year. In 2015, one billion people created a cat video. Let c be the number of cat videos, and y be the number of years since 2015.

The number of people watching cat videos doubles every hour. In 2015, one trillion people watched a cat video. Let w be the number of people watching cat videos, and y be the number of years since 2015.

Fang has a large rose garden. When the roses first bloomed, he initially picked 4 fresh roses. Each day after that, he picked 4 times as many roses as he picked on the previous day. Let R be the number of roses picked on day t.

Maria has a large tomato garden. When the tomatoes first ripened, she initially picked 3 tomatoes. Each day after that, she picked 5 tomatoes. Let O be the number of tomatoes picked on day t.

A newbon calf weighs 40 kilograms. Each week its weight increases by 5%. Let W be the wieght in kilograms of the calf after t weeks.

A basil plant starts out weighing 12.3 grams. The weight of the basil plant increases by 1.8 grams every day.

In 2000, there were one million educated people in the world. The number of educated people in the world increases by a factor of 1.8 every year. Let E be the number of educated people, and y be the number of years since 2000.

The polar ice sheets started out 0.2 kilometers deep. 9% of the polar ice sheets are melting each decade. Let d be the number of decades, and I be the depth of the polar ice sheets.

We started out with 6,200 living polar bears. The number of polar bears is decreasing by 1000 every year. Let P be the number of polar bears, and y be the years since we started.

The annual cost of your car insurance is initially 50,000 Philippine pesos. Each accident you have causes it to increase by 4,000 pesos. Let C be the cost of your car insurance, and a be the number of accidents you’ve had.

You are helping to organize a soccer tournament by registering the participating teams. Each week 6 teams register to participate. Let t be the number of teams who have registered, and w be the number of weeks.

The annual cost of your car insurance is $800 per year. Each year it decreases by $70. Let C be the cost of your insurance, and y be the number of years.

The amount of radioactive carbon in a fossil reduces by 50% every 5730 years. A certain dinosaur bone is observed to be 0.6 parts per million. Let Y be the number of 5730 year periods, and c be the concentration of carbon in parts per million.

The number of comments on a video increases by a factor of 6 every month. Taylor Swift had 12,000,000 comments in July. Let c be the number of comments, and m be the number of months since July.

Radoslaw works out regularly, and loses 4 kilograms each month. He started out weighing 130 kg. Let w be Radoslaw’s weight in kilograms, and m be the number of months.

Fidel has a rare coin work $550. Each year the coin’s value increases by 10%. Let v be the value of the coin, and y be the number of years elapsed.

Donald bought a car for 130,000 Mexican pesos. Each year the value of the car decreases by 10,000 pesos. Let M be the value of Donald’s car in Mexican pesos, and y be the number of years elapsed.

Tables

Linear Exponential Linear Exponential

? =

? =

x y

0 400

1 405

2 ?

3 415

4 420

5 425

x y

0 10

1 20

2 40

3 80

4 160

5 ?

Linear Exponential Linear Exponential

? = 0

? = 25

? = 78

? = 116

? = 9

? = 64

x y

0 10

1 8

2 6

3 4

4 2

5 ?

x y

0 400

1 200

2 100

3 50

4 ?

5 12.5

x y

0 81

1 ?

2 75

3 72

4 69

5 66

x y

0 256

1 221

2 186

3 151

4 ?

5 81

x y

0 81

1 27

2 ?

3 3

4 1

5 0.33

x y

0 256

1 ?

2 16

3 4

4 1

5 0.25

Rules of Exponents What you see Name of rule What you do Example Summary

What you see Name of rule What you do Example Summary

(

)

(

)

Work out

Work out

What is x?

What is x?

What is x?

What is x?

Lisa tried to simplify and expression step by step:

[( )( )] Step 1: ( )( ) Step 2: ( )( ) In which step did Lisa make a mistake? o Step 1 o Step 2 o Lisa did not make a mistake

Fred tried to simplify and expression step by step:

( ) Step 1: ( )

Step 2: ( )

Step 3: Step 4: In which step did Fred make a mistake? o Step 1 o Step 2 o Step 3 o Step 4 o Fred did not make a mistake

Which of the below is equivalent to

Equivalent Not

Equivalent

( )

⁄

⁄

Which of the below is equivalent to

Equivalent Not Equivalent

√

√

Rewrite:

( )

In the form

Simplify:

Rewrite:

In the form

Rewrite: ( )

using positive exponents

Rewrite:

In the form

Rewrite:

with positive exponents

Rewrite: ( )

In the form

The Function

Zoo Name:

Period:

Linear Lemmings

Domain:

Range:

x f(x) = x

-2 -2

-1 -1

0 0

1 1

2 2

Inverse Iguana

x f(x) = 1/x

-2 -1/2

-1 -1

0 ∞

1 1

2 1/2

Cube root Cuttlefish

x

-64 -4

-8 -2

0 0

8 2

64 4

Cubic Cougars

x

-2 -8

-1 -1

0 0

1 1

2 8

Absolute Value Alligators

x

-2 +2

-1 +1

0 0

1 +1

2 +2

Square Root Squirrels

x

-25 Undefined

-9 Undefined

0 0

9 3

25 5

Parabola Penguins

x

-2 +4

-1 +1

0 0

1 +1

2 +4

Horizontal Herrings

x f(x) = 4

-2 4

-1 4

0 4

1 4

2 4

Exponential Eagles

x f(x) = 3^x

-2 1/9

-1 1/3

0 1

1 3

2 9

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Domain:

Range:

Summary Name Domain Range Description

of table Description

of Graph Exponential

Eagles

Parabola Penguins

Linear Lemmings

Horizontal Herrings

Square Root

Squirrels

Name Domain Range Description of Table

Description of Graph

Absolute Value

Alligators

Cubic Cougars

Cube Root Cuttlefish

Inverse Iguana