Pre-Algebra Examples

Find the Exponential Function (-7,-3)
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 2.5
Solve the equation.
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Step 2.5.1
Rewrite the equation as .
Step 2.5.2
Divide each term in by and simplify.
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Step 2.5.2.1
Divide each term in by .
Step 2.5.2.2
Simplify the left side.
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Step 2.5.2.2.1
Cancel the common factor of .
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Step 2.5.2.2.1.1
Cancel the common factor.
Step 2.5.2.2.1.2
Divide by .
Step 2.5.2.3
Simplify the right side.
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Step 2.5.2.3.1
Move the negative in front of the fraction.
Step 2.5.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5.4
Simplify .
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Step 2.5.4.1
Rewrite as .
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Step 2.5.4.1.1
Rewrite as .
Step 2.5.4.1.2
Rewrite as .
Step 2.5.4.2
Pull terms out from under the radical.
Step 2.5.4.3
Raise to the power of .
Step 2.5.4.4
Rewrite as .
Step 2.5.4.5
Any root of is .
Step 3
Substitute each value for back into the function to find each possible exponential function.