Understanding Exponential Functions Through Graphs and Equations
Explore the concepts of exponential functions, their graphical representations, laws of exponents, solving equations, and practical applications. Learn how different bases affect the growth rate and the impact of negative signs on graphs.
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Presentation Transcript
Exponential Functions are functions which can be represented by graphs similar to the graph on the right
All base exponential functions are similar because they all go through the point (0,1), regardless of the size of their base number Exponential Functions are written in the form: y = abx a= constant b = base x = variable
When working with exponential equations, the Laws of Exponents still hold true = 3 3 + + 1 + = = 1 1 13 2 3 9 When solving exponential equations, it is important to have both sides of the equation set to the same base =125 25x = 5 5 2x ( ) 5 =3 x = 5 . 1 = 2 3 5 x 2 3 x
Yellow = 4x Green = ex Black = 3x Red = 2x
As you could see in the graph, the larger the base, the faster the function increased If we place a negative sign in front of the x, the graphs will be reflected(flipped) across the y-axis
Yellow = 4-x Green = e-x Black = 3-x Red = 2-x
By using Microsoft Excel, we can make a table of values and a graph of the data y = ex X-Value Y-Value -5 -4 -3 -2 -1 0 1 2 3 4 5 160.00 0.01 0.02 0.05 0.14 0.37 1.00 2.72 7.39 20.09 54.60 148.41 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00
We can also use Maple 7 to plot exponential graphs > plot (exp(x),x=-5..5);
The previous pages show what exponential growth looks like as a curve, but what happens in real life. You start with one item which replicates continuously.
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