Depreciation A company buys a machine for 225,000 dollars...

Depreciation A company buys a machine for 225,000 dollars that depreciates at a rate of $30 \%$ per year. Find a formula for the value of the machine after $n$ years. What is its value after 5 years?

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Key Concepts

Percentage Decay Rate

The percentage decay rate is the constant percentage reduction applied during each time interval in an exponential decay process. In depreciation scenarios, this rate indicates how much value the asset loses each period, which is then used to calculate its remaining value over time.

Initial Value

The initial value is the starting cost or value of an asset before any depreciation has taken place. This value serves as the baseline in depreciation calculations and is key to determining its subsequent worth over time.

Exponential Decay

Exponential decay describes a process where a quantity decreases by a constant percentage over equal time intervals. It is represented by formulas where the current value is the product of the initial value and a decay factor raised to a power corresponding to the number of time intervals.

Depreciation

Depreciation is the accounting process used to allocate the cost of a tangible asset over its useful life. It reflects the decrease in value of the asset over time due to factors like wear and tear or obsolescence, helping in financial reporting and tax calculations.

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