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 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

11 33 113 23 9

12525x 32 55x

32 55 x 32x 5.1x

Yellow = 4Yellow = 4xx Green = eGreen = exx

Black = 3Black = 3xx Red = 2Red = 2xx

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 = 4Yellow = 4-x-x Green = eGreen = e-x-x

Black = 3Black = 3-x-x Red = 2Red = 2-x-x

X-Value Y-Value-5 0.01-4 0.02-3 0.05-2 0.14-1 0.370 1.001 2.722 7.393 20.094 54.605 148.41

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By using Microsoft Excel, we can make a table of values and a graph of the data

y = ex

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.

Homework:

Pages ?

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