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

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 
an = 80,000(0.06)^n-1
an = 80,000(0.94)^n-1
an =80,000(0.94)^n
an = 80,000(0.06)^n

GPT-4o mini · Answer

To model the depreciation of the bakery's equipment over time, you should use an equation that accounts for the remaining value of the equipment after each year, based on the depreciation rate.

When an asset depreciates at a rate of 6% per year, it retains 94% of its value each year, which means we use a factor of 0.94 for the remaining value.

The equation that models this situation is:

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

In this equation:

$ a_n $ is the value of the equipment after $ n $ years,
$ 80,000 $ is the initial value of the equipment,
$ 0.94 $ represents the value remained after each year (100% - 6% = 94% or 0.94),
$ n $ is the number of years.

So the correct choice is:

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