a small business owner buys a truck for $20,000 to transport supplies for her business. She anticipates that she will use the truck for 5 years and that the truck will be worth $10,000 in 5 years. She plans to claim a depreciation tax credit using the straight-line depreciation method approved by the Internal Revenue Service. This means that if V is the value of the truck at time t, then a linear equation is used to relate V and t.
(a) Find a linear equation that models the depreciated value V of the truck t years since it was purchased.
(b) What is the rate of depreciation?
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To find a linear equation that models the depreciated value V of the truck t years since it was purchased, we can use the straight-line depreciation method approved by the Internal Revenue Service.
The straight-line depreciation method assumes that the value of the truck decreases by an equal amount each year over its useful life.
Given that the truck was purchased for $20,000 and it is estimated to be worth $10,000 after 5 years, we can calculate the annual depreciation amount.
Depreciation amount = (Initial value - Final value) / Useful life
Depreciation amount = ($20,000 - $10,000) / 5 = $2,000 per year
Now, let's formulate the linear equation using the depreciation amount.
The equation for straight-line depreciation is:
V = Initial value - (Depreciation amount * t)
Where:
V is the value of the truck at time t
Initial value is the original purchase price ($20,000)
t is the number of years since the truck was purchased
Depreciation amount is the annual depreciation amount ($2,000)
(a) Therefore, the linear equation that models the depreciated value V of the truck t years since it was purchased is:
V = $20,000 - ($2,000 * t)
(b) The rate of depreciation in this case is $2,000 per year.