Initial Value 1st 2nd 3rd 4th

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

SITUATION 1 Snowfall

X y

TABLE

GRAPH

SEQUENCE

MULTIPLIER(rate of change)

Y-intercept (initial value)

NEXT-NOW STATEMENT Practical Domain

Practical Range

EQUATION

12

Y = 1(2)x

or y = 2x

Hour after midnight

Number of Bacterium

012

3

21

48

X 2X 2

1X 2 X 2 X 2 X 2

2 4 8 16

NEXT=NOW*2; starting at 1All non-negative numbers

All numbers at least one

X 2

Plot points from graph

SITUATION 2 Amount of Flowers

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER (rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

Y = 6(1/3)x

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

1/36

0 61 22 .667 =

2/33 .222 =

2/9

6 2 .667 = 2/3

.222 = 2/9

.0741 = 2/27

-1 1 2 3 4

1

2

3

4

5

6

x

y

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

Nonneg. nos.nonneg nos.

≤ 6

SITUATION 3 Savings Account

X y

0 100

1 105

2 110.25

3 115.76

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER (rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

1.05 100

y = 100(1.05)x

100 105 110.25

115.76

121.55

-1 1 2 3 4 5 6 7 8

20

40

60

80

100

120

140

160

x

y

NEXT = NOW *(1.05); Start at 100

Nonneg. nos.y ≥ 100

SITUATION 4 Stock Investment

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

88 96.80 106.48

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

1.1 80

y = 80(1.1)x

0 801 882 96.803 106.4

8

80 117.13

-1 1 2 3 4 5 6 7 8

20

40

60

80

100

120

140

160

x

y

NEXT = NOW *(1.1); Start at 80

Nonneg. nos.y ≥ 80

SITUATION Value of a Car

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

17,000 14,450 12282.50

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

.85 20,000

y = 20000(.85)x

0 20,0001 17,000

2 14,4503 12,282.5

0

20,000

10,440.13

-3 -2 -1 1 2 3 4 5 6 7 8 9 10

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

x

y

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

Nonneg. nos.nonneg nos.

≤ 20000

SITUATION 6 Evaporation of Water

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER (rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

1/48

y = 8(1/4)x

0 81 22 .53 .125

8 2 .5 .125 .03125

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

Nonneg. nos.Nonneg.

nos.≤ 8

SITUATION 7 Attendance Increase

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

NEXT=NOW*1.5; starting at 16

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

1.5 16

y = 16(1.5)x

0 161 242 363 54

16 24 36 54 81

-3 -2 -1 1 2 3 4 5 6 7 8 9

5101520253035404550556065707580859095100105110115120125130135

x

y

Nonneg. nos.y ≥ 16

SITUATION 8 Population of a Village

X Years since 2010

YPopulation

1 12400

2 13020

TABLE

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

1.05 11,810

y = 11,810(1.05)x0 11,810

3 13,672

11,810 12,40013,02013,67214,353

NEXT = NOW *(1.05); Start at 11810

-5 5 10 15 20 25 30 35 40 45 50 55 60

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

110000

120000

x

y

Nonneg. nos.y ≥ 11810

SITUATION 9 Volume of Balloon

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER 3(rate of change)

Y-intercept 2/3 (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

y = 2/3(3)x0 2/3

1 22 63 18

2/3 2 6 18 54

NEXT = NOW *3; Start at 2/3

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7-1

12345678910111213141516171819

x

y

Nonneg. nos.y ≥ 2/3

The value of an antique vase was $1800 in 2010. Each year, it increased its value by 8.5%

SITUATION 10

X y

TABLE

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER (rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

1.085 1800

y = 1800(1.085)x

0 18001 19532 21193 2299.1

1800 1953 2119 2299.12494.5

-4 -3 -2 -1 1 2 3 4 5 6 7

1000

2000

3000

4000

x

y

NEXT = NOW *1.085; Start at 1800

Nonneg. nos.y ≥ 1800

SITUATION 11 Number of Friends on a Social Media Network

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

6 18 54

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT

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

3 2

y = 2(3)x

0 21 62 183 54

2 162

-1 1 2 3 4 5

5

10

15

20

25

30

35

40

45

50

55

60

65

70

x

y

NEXT = NOW *3; Start at 2

SITUATION 12 ______________________________

X y

TABLE

GRAPH

SEQUENCEInitial Value 1st 2nd 3rd 4th

MULTIPLIER(rate of change)

Y-intercept (initial value)

Practical Domain

Practical Range

EQUATION

NEXT-NOW STATEMENT