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)

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(0.06)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−1
a subscript n baseline equals 80,000 left parenthesis 0.94 right parenthesis superscript n minus 1 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

GPT-4o mini · Answer

To model the depreciation of the bakery's equipment, you want to use an equation that reflects the value of the equipment decreasing over time at a rate of 6 percent per year.

The equipment value decreases by 6% each year, which means that it retains 94% of its value (100% - 6% = 94%). Therefore, the value of the equipment after each year can be expressed as:

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

where:

$ a_n $ is the value of the equipment after $ n $ years.
$ 80,000 $ is the initial value of the equipment.
$ 0.94 $ is the factor representing the 94% of the value retained each year.
$ n $ represents the number of years since the bakery opened.

So the correct equation from the provided responses is:

$ a_n = 80,000(0.94)^n $