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

GPT-4o mini · Answer

To model the depreciation of the equipment over time, you use the formula for exponential decay. The depreciation rate is given as 6% per year, which means that after one year, the value of the equipment is 94% of its original value (because $100% - 6% = 94%$).

Using this information, the correct equation to model the value of the equipment $a_n$ after $n$ years is:

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

So, the correct response would be:

an=80,000(0.94)n