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SITUATION 1 Snowfall

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SITUATION 1 Snowfall

At midnight, there was 1 bacterium. The number of bacterium doubled every hour

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

2

1

TABLE

EQUATION

Hour

after midnight

Number

of Bacterium

Y = 1(2)x

or y = 2x

0

1

X 2

2

1

X 2

2

4

X 2

3

8

SEQUENCE

Plot points from graph

1

2

4

8

16

X 2

X 2

X 2

X 2

NEXT-NOW STATEMENT

Practical Domain

All non-negative numbers

Practical Range

NEXT=NOW*2; starting at 1

All numbers at least one

SITUATION 2 Amount of Flowers

There are 6 flowers in a vase. After each day 1/3 of the flowers are left.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

6

1/3

TABLE

EQUATION

Y = 6(1/3)x

0

6

1

2

2

.667 = 2/3

3

.222 = 2/9

SEQUENCE

.667 = 2/3

.222 = 2/9

.0741 = 2/27

6

2

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *(1/3); Start at 6

nonneg nos. ≤ 6

Practical Range

SITUATION 3 Savings Account

Joe has $ 100 in his savings account which earns interest at a rate of 5 % per year.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

100

1.05

TABLE

EQUATION

y = 100(1.05)x

SEQUENCE

110.25

115.76

100

105

121.55

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *(1.05); Start at 100

y ≥ 100

Practical Range

SITUATION 4 Stock Investment

Sue has $ 80 that she invests in stock that is growing at a rate of 10 % per year.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

1.1

80

TABLE

EQUATION

y = 80(1.1)x

0

80

1

88

2

96.80

3

106.48

SEQUENCE

80

117.13

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *(1.1); Start at 80

y ≥ 80

Practical Range

SITUATION Value of a Car

Tom has a $ 20,000 car that depreciates at a rate of 15 % per year.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

.85

20,000

TABLE

EQUATION

y = 20000(.85)x

0

20,000

1

17,000

2

14,450

3

12,282.50

SEQUENCE

20,000

10,440.13

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

nonneg nos.

≤ 20000

NEXT = NOW *(.85); Start at 20000

Practical Range

SITUATION 6 Evaporation of Water

Eight ounces of water is in a glass. At the end of each day ¼ of the water is left.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

8

1/4

TABLE

EQUATION

y = 8(1/4)x

0

8

1

2

2

.5

3

.125

SEQUENCE

8

2

.5

.125

.03125

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

Nonneg. nos.

≤ 8

NEXT = NOW *(1/4); Start at 8

Practical Range

SITUATION 7 Attendance Increase

On the opening day of a carnival, 16 people attended. After opening day, attendance increased by 50 %.

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

1.5

16

TABLE

EQUATION

y = 16(1.5)x

0

16

1

24

2

36

3

54

SEQUENCE

16

24

36

54

81

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

y ≥ 16

NEXT=NOW*1.5; starting at 16

Practical Range

SITUATION 8 Population of a Village

In a certain year, the population of a village is 11, 810. The population grows at a rate of 5 % per year.

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

1.05

11,810

TABLE

EQUATION

y = 11,810(1.05)x

11,810

0

13,672

3

SEQUENCE

11,810

12,400

13,020

13,672

14,353

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *(1.05); Start at 11810

y ≥ 11810

Practical Range

SITUATION 9 Volume of Balloon

The volume of a balloon is 2/3 liter. As each gust of helium is added, the balloon triples its volume.

GRAPH

MULTIPLIER 3

(rate of change)

Y-intercept 2/3

(initial value)

TABLE

EQUATION

y = 2/3(3)x

2/3

0

1

2

2

6

3

18

SEQUENCE

2/3

2

6

18

54

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *3; Start at 2/3

y ≥ 2/3

Practical Range

SITUATION 10

The value of an antique vase was $1800 in 2010. Each year, it increased

its value by 8.5%

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

1.085

1800

TABLE

EQUATION

y = 1800(1.085)x

0

1800

1

1953

2

2119

3

2299.1

SEQUENCE

1800

1953

2119

2299.1

2494.5

NEXT-NOW STATEMENT

Practical Domain

Nonneg. nos.

NEXT = NOW *1.085; Start at 1800

y ≥ 1800

Practical Range

SITUATION 11 Number of Friends on a Social Media Network

Bonnie has been on a social network. When she started, she was chatting with 2 friends. Her number of friends tripled every hour.

GRAPH

MULTIPLIER

(rate of change)

3

Y-intercept

(initial value)

2

TABLE

EQUATION

y = 2(3)x

0

2

1

6

2

18

3

54

SEQUENCE

2

162

NEXT-NOW STATEMENT

Practical Domain

NEXT = NOW *3; Start at 2

Practical Range

SITUATION 12 ______________________________

GRAPH

MULTIPLIER

(rate of change)

Y-intercept

(initial value)

TABLE

EQUATION

SEQUENCE

NEXT-NOW STATEMENT

Practical Domain

Practical Range