Precalculus Examples

Find the Average Rate of Change y=(1.06)^(8t)
Step 1
Write as a function.
Step 2
Consider the difference quotient formula.
Step 3
Find the components of the definition.
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Step 3.1
Evaluate the function at .
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Step 3.1.1
Replace the variable with in the expression.
Step 3.1.2
Simplify the result.
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Step 3.1.2.1
Apply the distributive property.
Step 3.1.2.2
The final answer is .
Step 3.2
Find the components of the definition.
Step 4
Plug in the components.
Step 5
Simplify the numerator.
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Step 5.1
Rewrite as .
Step 5.2
Rewrite as .
Step 5.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.4
Simplify.
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Step 5.4.1
Rewrite as .
Step 5.4.2
Rewrite as .
Step 5.4.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.4.4
Simplify.
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Step 5.4.4.1
Rewrite as .
Step 5.4.4.2
Rewrite as .
Step 5.4.4.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 6