Final answer:
Using the formula for exponential decay V = P(1 - r)^t, where P is the present value of the appliance ($2,740), r is the depreciation rate (28.5% or 0.285), and t is the time in years (10), the appliance's value after 10 years is approximately $157.01.
Step-by-step explanation:
To calculate the value of an appliance after 10 years with an annual depreciation rate of 28.5%, we can use the formula for exponential decay. The formula is V = P(1 - r)^t, where V is the future value of the appliance, P is the present value, r is the rate of depreciation (expressed as a decimal), and t is the time in years.
The present value of the appliance is $2,740. The depreciation rate per year is 28.5%, which as a decimal is 0.285. We want to find the value after 10 years. Plugging these into our formula, we get:
V = $2,740(1 - 0.285)^10
Calculating the value inside the parentheses first (1 - 0.285) gives us 0.715. Now we'll raise 0.715 to the power of 10:
V = $2,740(0.715)^10
Calculating 0.715 to the power of 10 gives us approximately 0.0573. Finally, we multiply this by the present value:
V = $2,740 × 0.0573 ≈ $157.01
Therefore, if the homeowner's estimate of the annual depreciation rate is accurate, the appliance currently valued at $2,740 will be worth approximately $157.01 in 10 years.