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 situation where the bakery's equipment depreciates at a rate of 6 percent per year, you want to express the value of the equipment after \( n \) years.

The value after each year will be the original price multiplied by the depreciation factor. Since the equipment depreciates by 6 percent, it retains 94 percent of its value each year, which can be represented as \( 0.94 = 1 - 0.06 \).

Thus, the appropriate sequence modeling the value of the equipment after \( n \) years would be:

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

This means that the value of the equipment after \( n \) years is equal to the initial value multiplied by \( 0.94 \) raised to the power of \( n \).

So, the correct choice from your options is:

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