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(0.06)n−1
a subscript n baseline equals 80,000 left parenthesis 0.06 right parenthesis superscript n minus 1 baseline

an=80,000(0.94)n

Answer 1

To model the depreciation of the bakery's equipment at a rate of 6 percent per year, you would typically use the formula for exponential decay. The value of the equipment after \(n\) years can be represented as:

\[
a_n = a_0 \cdot (1 - r)^n
\]

where:
- \(a_n\) is the value after \(n\) years,
- \(a_0\) is the initial value ($80,000 in this case),
- \(r\) is the depreciation rate (0.06 for 6 percent),
- \(n\) is the number of years.

In this case, the equation simplifies to:

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

This reflects that the value decreases by 6% every year, leaving 94% of its value.

From your provided options, the correct equation to describe this situation is:

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

So the correct choice is:

**an = 80,000(0.94)^n**.