Question

A local bakery opened with new equipment worth $80,000. Ten years later, the owners’ accountants told them that their equipment had depreciated at a rate of 6 percent per year. Which equation would you use to create a sequence modeling this situation?(1 point)
Responses

an=80,000(0.94)n−1
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n minus 1 baseline

an=80,000(0.06)n
a subscript n baseline equals 80,000 left parenthesis 0.06 right parenthesis superscript n baseline

an=80,000(0.94)n
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n baseline

an=80,000(0.06)n−1

Answer 1

To model the depreciation of the equipment using an exponential decay function, you need to incorporate the rate at which the equipment depreciates. Since the equipment depreciates at a rate of 6 percent per year, we can represent the value of the equipment after \( n \) years.

The value of the equipment after \( n \) years can be calculated using the formula:

\[
a_n = 80,000 \times (1 - 0.06)^n
\]

which simplifies to:

\[
a_n = 80,000 \times (0.94)^n
\]

This accounts for the 6% depreciation each year (since \( 1 - 0.06 = 0.94 \)).

Based on the given responses, the correct form of the equation would be:

**\( a_n = 80,000(0.94)^n \)**

This option reflects the correct depreciation model and represents the value of the equipment after \( n \) years.

So the correct answer is:

**\( a_n = 80,000(0.94)^n \)**.