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SITUATION 1 Snowfall

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

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SITUATION 1 Snowfall

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. SITUATION 12 ______________________________ GRAPH MULTIPLIER (rate of change) Y-intercept (initial value) TABLE EQUATION SEQUENCE NEXT-NOW STATEMENT Practical Domain Practical Range

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