Finite Math Examples

Find the Exponential Function (-8,1)
Step 1
To find an exponential function, , containing the point, set in the function to the value of the point, and set to the value of the point.
Step 2
Solve the equation for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Rewrite the expression using the negative exponent rule .
Step 2.3
Find the LCD of the terms in the equation.
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Step 2.3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.3.2
The LCM of one and any expression is the expression.
Step 2.4
Multiply each term in by to eliminate the fractions.
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Step 2.4.1
Multiply each term in by .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Rewrite the expression.
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Multiply by .
Step 2.5
Solve the equation.
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Step 2.5.1
Rewrite the equation as .
Step 2.5.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5.3
Any root of is .
Step 2.5.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.5.4.1
First, use the positive value of the to find the first solution.
Step 2.5.4.2
Next, use the negative value of the to find the second solution.
Step 2.5.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
Substitute each value for back into the function to find each possible exponential function.