The given asset depreciates at a rate of approximately 12% per time period, leading to a gradual decline in value over time, as described by the function f(x) = 27000 × (0.88)^4.
The given function represents a depreciating asset, where f(x) represents the value of the asset at time x. The function is f(x) = 27000 * (0.88)^4.
In this function:
The initial value of the asset is $27,000.
The base, 0.88, represents the depreciation factor.
The exponent, 4, represents the number of time periods.
The depreciation rate can be determined by examining the base of the exponential term, which is 0.88. The depreciation rate is the factor by which the value of the asset decreases over each time period.
In this case, the depreciation rate is 1 - 0.88, as the value is decreasing. Therefore, the depreciation rate is 1 - 0.88 = 0.12 or 12%.
So, the asset depreciates by approximately 12% each time period, and the function models the decreasing value of the asset over time.