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

GPT-4o mini · Answer

To model the depreciation of the bakery's equipment over time with a 6% depreciation rate, we need to use the concept of annual exponential decay. The equipment loses 6% of its value each year, which means that 94% of its value remains after each year. This means that each year, the value is multiplied by 0.94.

The equation for the value of the equipment after $n$ years can be modeled as:

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

So, the correct choice from the options provided is:

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

This represents the value of the equipment $n$ years after it was purchased, accounting for the annual depreciation rate.