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Growth Graphing Exponential Equations Two types of exponential equations Decay With a plant, the leaves grow in the upward (+y) direction and the roots grow in the downward (-y) direction. With an exponential function, growth is anythingmoving away from a horizontal axis in either theupward or downward direction. The graph gets morevertical. This represents an increase over time. Graphing Exponential Equations Growth x With radioactive material, the element decreases in its amount present over time. With an exponential function, decay is anything moving towards the horizontal axis from either theupward or downward direction. The graph gets morehorizontal. This represents a decrease over time. Graphing Exponential Equations Decay x 0 2 -2 4 -4 General form when there is an offset (h, k) y = a•(b)x-h + k b: is the base and determines if the function grows or decays 0 < b < 1 Graphing Exponential Equations Decay Growth y = a•(b)x b > 1 Commom Form General form when there is an offset (h, k) Identifying exponentials using 3 characteristics: 1. What is "k"? 2. What is "b"? 3. What is "a"? y = a•(b)x-h + k "a" is the multiplier. "b" is the base. "k" is the location of the asymptote. Graphing Exponential Equations The base indicates growth or decay.Growth: b > 1Decay: 0 < b < 1 Exponential functions are asymptotic with a horizontal line. This means there is a horizontal line that the function gets close to but never crosses. The multiplier indicates if the function is drawn above the asymptote or below the asymptote.+a drawn above-a drawn below y = a•(b)x Commom Form Growth Growth: b > 1 Growth: b > 1 +a drawn above -a drawn below Graphing Exponential Equations General form when there is an offset (h, k) y = a•(b)x-h + k k is the horizontal asymptote +a drawn above Decay: b < 1 Decay: b < 1 -a drawn below Decay Graphing Exponential Equations | | Look at the graph, when x = 0 y = -1/2 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | 1 Graphing Exponential Equations | | Look at the graph, when x = 0y = 4 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn above the asymptote so a is This is decay so b | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 2.5so a = 0.5 Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b | | | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 7so a = 5 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b | | | | 1 Graphing Exponential Equations | | Look at the graph, when x = 0y = -3 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | 1 Graphing Exponential Equations | | Look at the graph, when x = 0y = -4 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 4so a = Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b | | 1 | | Graphing Exponential Equations | | Look at the graph, when x = 0y = -1/3 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 2so a = 4 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b | | | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 2so a = Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b | | 1 | | Graphing Exponential Equations This is drawn below the asymptote so a is Look at the graph,when x = 0, y = -4so a = -4 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b | | | | 1 Graphing Exponential Equations | | Look at the graph, when x = 0y = -2 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | 1 Graphing Exponential Equations This is drawn below the asymptote so a is Look at the graph,when x = 0, y = -1/4so a = -1/4 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b 1 | | | | Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 3so a = Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b | | 1 | | Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 4so a = 2 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b | | | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 18so a = Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b | | | | 1 Graphing Exponential Equations This is drawn below the asymptote so a is Look at the graph,when x = 0,y = 1.75so a = -0.25 Asymptote is at k = General Form: y = a•(b)x-h + k This is decay so b | | | | 1 Graphing Exponential Equations This is drawn above the asymptote so a is Look at the graph,when x = 0, y = 8so a = Asymptote is at k = General Form: y = a•(b)x-h + k This is growth so b 1 | | | | Graphing Exponential Equations | | Look at the graph, when x = 0y = 1/2 so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn above the asymptote so a is This is decay so b | | 1 Graphing Exponential Equations Look at the graph, when x = 0y = -2.25so a = General Form: y = a•(b)x-h + k Asymptote is at k = This is drawn below the asymptote so a is This is growth so b | | | | 1 |