Name Date #93 pg. 1. Decay: Tables, Graphs & Evaluating Equations. Complete the tables and graph each function, then answer the questions.

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1 Name Date #93 pg. 1 Decay: 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? b) What is the shape of all three graphs? c) What do you notice about the multiplier/common ratio? Exponential Decay Functions x x 1 4) Does the equation y 3 model exponential growth or exponential decay? 5 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?

5) Identify each function as Linear, growth, or

a) b) c) d) x 1 6) Which graph matches the equation

Factor (b) What is the ending time when x =-2?

2 5) Identify each function as Linear, growth, or decay. a) b) c) d) x 1 6) Which graph matches the equation y 2? 2 a) b) Growth or Decay (a) Growth or Decay Factor (b) What is the ending time when x =-2? c) d) Write an exponential function for each table below and find the end time. x y x y x y Growth Factor 0 9 Growth Factor Growth Factor

3 #93 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 Growth Factor 0 25 Growth Factor Growth Factor

4 6) A citrus orchard has 180 orange trees. A fungus attacks the trees. Each month after the attack, the number of living trees is decreased by one-third. If x represents the time, in months, and y, represents the number of living tress, which graph best represents this situation over 5 months? Growth or Decay Growth or Decay Factor Function What is the ending time when x =2 (month)? 7) Some pests are attacking Mrs. Gonzalez s vegetable garden. She sprayed her garden with a bug spray to kill off the bugs, but not harm her vegetables. The directions warn not to over spray because the dose can cause the plant tolerance to become dangerously low. Using the function to determine the plant tolerance for the first 4 sprays. x

5 Name Date #93 pg. 1 Decay: Tables, Graphs & Evaluating Equations Complete the tables and graph each function, then answer the questions. 1) 2) (0,1) 2) (0,1) Observations: a) What pattern do yo notice on all three tables in prolem #1, 2, and 3? The y values are decreasing as the x values increase b) What is the shape of all three graphs? Backwards J-shape Arching downward, but never crosses the x-axis (0,2) c) What do you notice about the multiplier/common ratio? They are all positive fractions, thus between 0 and 1 Exponential Decay Functions x End Value or y-intercept or Zero Decay Factor or Multiplier or Common Ratio Time Stages x 1 4) Does the equation y 3 model exponential growth or exponential decay? Decay 5 a) What is initial value (a)? 3 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,.12) if x = -2? (-2, 75)

6 5) Identify each function as Linear, growth, or decay. a) b) c) d) Exponential Decay Exponential Growth Linear Exponential Decay x 1 6) Which graph matches the equation y 2? 2 a) b) Growth or Decay decay (a) 2 Growth or Decay Factor (b) What is the ending time when x =-2? (-2,8) c) d) Write an exponential function for each table below and find the end time. x y x y x y Growth Factor 0 9 Growth Factor Growth Factor.00064

7 ANSWER KEY #93 pg. 2 Complete the following tables and graph each function. 1) 2) (0,3) 3) (0,1) 4) (0,5) (0,6) 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 Growth Factor 0 25 Growth Factor Growth Factor 3.91

8 6) A citrus orchard has 180 orange trees. A fungus attacks the trees. Each month after the attack, the number of living trees is decreased by one-third. If x represents the time, in months, and y, represents the number of living tress, which graph best represents this situation over 5 months? Growth or Decay decay 180 Growth or Decay Factor Function What is the ending time when x =2 (month)? (2,20) 7) Some pests are attacking Mrs. Gonzalez s vegetable garden. She sprayed her garden with a bug spray to kill off the bugs, but not harm her vegetables. The directions warn not to over spray because the dose can cause the plant tolerance to become dangerously low. Using the function to determine the plant tolerance for the first 4 sprays. x examples

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