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GRAPHS OF EXPONENTIAL FUNCTIONS
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By Nancy Marcus
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In this section we will illustrate, interpret, and discuss the
graphs of exponential functions. We will also illustrate how
you can use graphs to HELP you solve exponential problems.
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Solving an equation from a graph. When we solve an equation
algebraically, we set the equation equal to zero and find those
values that cause the equation to equal zero. When we solve
an equation graphically, we look for points of intersection.
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If there is one equation, we look to see where the graph crosses
the x-axis. The x-intercepts are the solutions to the equation.
The x-intercepts are those values of x that cause the function
value to be zero.
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If you are solving two equations graphically, you have two options.
You can graph both equations and determine the value of x at
the point(s) of intersection. You can also create a new graph
by subtracting one function from another, graph the new function,
and find the x-intercepts.
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In the following examples, we will solve the equations algebraically
and graphically.
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Example 15:** Solve the equation
for x algebraically and graphically.

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Algebraically:
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1.Take the natural logarithm of both sdies of the equation. The left side of the equation can be simplified to x. The actual value of x is and the approximate value of x is 1.609438.

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Graphically - Method 1:
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1.Graph
and graph *g*(*x*)=5
on the same coordinate axis and find the
point(s), if any, of intersection.

2.The graph intersection at one point. (1.609438, 5). The solution is the value of x, or x = 1.609438.

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Graphically - Method 2:**

1.Subtract 5 from both sides of the equation to have .

2.Call the left side of the equation f(x) and graph f(x). Call the right side of the equation h(x) and graph h(x). Since the right side of the equation is nothing more than the x-axis, you will be looking for the x intercepts on the graphs of .

3.The graph of f(x) crosses the x-axis at x = 1.609438.

If you would like to review another example, click on
*Example. *

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