Precalculus Examples

Find the Average Rate of Change 3280(1.0117)^(12t)
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
Multiply by .
Step 5.2
Rewrite in a factored form.
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Step 5.2.1
Factor out of .
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Step 5.2.1.1
Factor out of .
Step 5.2.1.2
Factor out of .
Step 5.2.1.3
Factor out of .
Step 5.2.2
Rewrite as .
Step 5.2.3
Rewrite as .
Step 5.2.4
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 5.2.5
Simplify.
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Step 5.2.5.1
Rewrite as .
Step 5.2.5.2
Rewrite as .
Step 5.2.5.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.2.5.4
Simplify.
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Step 5.2.5.4.1
Rewrite as .
Step 5.2.5.4.2
Rewrite as .
Step 5.2.5.4.3
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 5.2.5.5
Multiply by by adding the exponents.
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Step 5.2.5.5.1
Use the power rule to combine exponents.
Step 5.2.5.5.2
Add and .
Step 5.3
Simplify each term.
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Step 5.3.1
Multiply the exponents in .
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Step 5.3.1.1
Apply the power rule and multiply exponents, .
Step 5.3.1.2
Apply the distributive property.
Step 5.3.1.3
Multiply by .
Step 5.3.1.4
Multiply by .
Step 5.3.2
Multiply the exponents in .
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Step 5.3.2.1
Apply the power rule and multiply exponents, .
Step 5.3.2.2
Multiply by .
Step 6