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

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(0.94)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(0.06)n

Answer 1

To model the depreciation of the bakery's equipment, we use the concept of exponential decay. Given that the equipment depreciates at a rate of 6% per year, the value of the equipment after \( n \) years can be calculated using the initial value (which is $80,000) and the decay factor (which is \( 1 - 0.06 = 0.94 \)) raised to the power of \( n \).

The correct equation to model the situation is:

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

This indicates that after \( n \) years, the value of the equipment is the initial value multiplied by the decay factor raised to the number of years.

Thus, the correct response is:

an=80,000(0.94)n
\( a_n = 80,000 (0.94)^n \)