Name Date #92 pg. 1. Growth: Tables, Graphs & Evaluating Equations Complete the tables and graph each function, then answer the questions.

Transcription

1 Name Date #92 pg. 1 Growth: Tables, Graphs & Evaluating Equations Complete the tables and graph each function, then answer the questions. 1) 2) 2) Observations: a) What pattern do yo notice on all three tables in prolem #1, 2, and 3? The y values are increasing as the x values increase b) What is the shape of all three graphs? c) What do you notice about the multiplier/common ratio? Exponential Growth Functions x 4) Does the equation y 64 x model exponential growth or exponential decay? a) What is initial value (a)? b) What is the growth or decay factor (b)? c) What is the ending time d) What is the ending time if x = 2? if x = -2?

2 5) Identify each function as Linear, growth, or decay. a) b) c) d) 6) Which graph matches the equation 1 2 Growth or Decay x y? 4 (a) Growth or Decay Factor (b) What is the ending time when x = 4? Write an exponential function for each table below and find the end time. x y x y x y

3 #92 pg. 2 Complete the following tables and graph each function. 1) 2) 3) 4) Identify each function as linear, growth or decay. 5E) 5F) 5G) 5H) Write an exponential function for each table below and find the end time. x y x y x y

4 6) The graph represents the number of visitors (y) to a new art gallery after months (x). Growth or Decay (y-intercept) Growth or Decay Factor (Common Ratio) Write an exponential function that represents this situation. Approximate the number of visitors after 5 months? 8) There is a population of 15 bacteria the pool. As the temperature gets warmer the bacteria grows. Using the function, determine how much bacteria you will have in 5 days. x

5 Name Date key #92 pg. 1 Growth: Tables, Graphs & Evaluating Equations Complete the tables and graph each function, then answer the questions. 1) 2) (0,1) 2) (0,1) 4 Observations: a) What pattern do yo notice on all three tables in prolem #1, 2, and 3? The y values are increasing as the x values increase b) What is the shape of all three graphs? J-shape Arching upward, but never crosses the x-axis (0,3) c) What do you notice about the multiplier/common ratio? They are all positive numbers, thus greater than 1 Exponential Growth Functions x End Value or y-intercept or Zero or Multiplier or Common Ratio Time Stages 4) Does the equation y 64 x model exponential growth or exponential decay? Growth a) What is initial value (a)? 6 b) What is the growth or decay factor (b)? c) What is the ending time d) What is the ending time if x = 2? (2, 96) if x = -2? (-2,.375)

6 5) Identify each function as Linear, growth, or decay. a) b) c) d) Linear Exponential Growth Exponential Growth Exponential Decay 6) Which graph matches the equation 1 2 Growth or Decay Growth x y? A 4 (a) Growth or Decay Factor (b) What is the ending time when x = 4? (4,4) Write an exponential function for each table below and find the end time. x y x y x y

7 ANSWER KEY #92 pg. 2 Complete the following tables and graph each function. 1) 2) (0,1) 5 3) (0,1) 2.5 4) (0,3) 4 (0,2) 4 Identify each function as linear, growth or decay. 5E) 5F) 5G) 5H) Write an exponential function for each table below and find the end time. x y x y x y

8 6) The graph represents the number (y) of visitors to a new art gallery after (x) months. Growth or Decay Growth (y-intercept) (0,40) Growth or Decay Factor (Common Ratio) Write an exponential function that represents this situation. Approximate the number of visitors after 5 months? 8) There is a population of 15 bacteria the pool. As the temperature gets warmer the bacteria grows. Using the function, determine how much bacteria you will have in 5 days. x examples