To model the depreciation of the bakery's equipment, we want to represent how the value of the equipment decreases over time. The equipment originally cost $80,000 and depreciates at a rate of 6% per year.
When an asset depreciates at a certain percentage (in this case, 6%), it retains a percentage of its value each year. Specifically, after each year, it retains (100% - 6%) = 94% of its value from the previous year.
The formula to calculate the value of an asset after \( n \) years of depreciation can be written as:
\[ V = P(1 - r)^n \]
Where:
- \( V \) is the value after \( n \) years,
- \( P \) is the initial value (in this case, $80,000),
- \( r \) is the rate of depreciation (0.06), and
- \( n \) is the number of years.
Since the equipment retains 94% of its value each year, we can express this mathematically as:
\[ V = 80,000 (0.94)^n \]
Now, looking at the options provided, we see that:
A. \( a_n = 80,000(0.94)^{(n-1)} \)
B. \( a_n = 80,000(0.06)^n \)
C. \( a_n = 80,000(0.94)^n \)
D. \( a_n = 80,000(0.06)^{(n-1)} \)
The correct equation should reflect that the value after \( n \) years decreases at the rate of 94% retained, so:
The correct answer is: C. \( a_n = 80,000(0.94)^n \).
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