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

an=80,000(0.06)n−1
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(0.06)n

GPT-4o mini · Answer

To model the depreciation of the bakery's equipment over time, we need to account for the depreciation rate of 6% per year. The residual value after each year can be found by multiplying the initial value by the remaining percentage of value after depreciation. Since the equipment depreciates by 6%, it retains 94% of its value each year (100% - 6% = 94%).

The equation that models the value of the equipment after $ n $ years is:

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

This means that $ a_n $ is the value of the equipment after $ n $ years, 80,000 is the initial cost, and $ (0.94)^n $ represents the value retained after $ n $ years of 6% depreciation.

Therefore, the correct equation to create a sequence modeling this situation is:

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