1527 exponential functions
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The document discusses exponential functions, highlighting their common characteristics and equations in the form y = ab^x. It explains the importance of having both sides of an exponential equation set to the same base and provides examples of how different bases affect the graph's growth rate. Additionally, it mentions the use of Microsoft Excel and Maple 7 for plotting exponential graphs and illustrates the concept of exponential growth in real life.
1527 exponential functions
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- 2. Exponential Functions are functions which can be represented by graphs similar to the graph on the right
- 3. 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
- 4. When solving exponential equations, it is important to have both sides of the equation set to the same base When working with exponential equations, the Laws of Exponents still hold true =⋅ −+ ππ 11 33 =−++ ππ 11 3 =2 3 9 →=12525x ( ) →= 32 55 x →= 32 55 x →= 32x 5.1=x
- 5. Yellow = 4Yellow = 4xx Green = eGreen = exx Black = 3Black = 3xx Red = 2Red = 2xx
- 6. 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
- 7. Yellow = 4Yellow = 4-x-x Green = eGreen = e-x-x Black = 3Black = 3-x-x Red = 2Red = 2-x-x
- 8. X-Value Y-Value -5 0.01 -4 0.02 -3 0.05 -2 0.14 -1 0.37 0 1.00 1 2.72 2 7.39 3 20.09 4 54.60 5 148.41 0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00 160.00 By using Microsoft Excel, we can make a table of values and a graph of the data y = ex
- 9. We can also use Maple 7 to plot exponential graphs > plot (exp(x),x=-5..5);
- 10. 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.