A delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. Suppose the truck depreciates at a rate of $7,200 per year, formulate a function ƒ(t) that can be used to estimate the truck's depreciated value after t years.
Let's assume that the depreciated value of the truck after t years is represented by the variable D(t).
Given that the truck depreciates at a rate of $7,200 per year, we can say that the depreciated value after t years is equal to the initial value of the truck minus the depreciation for t years:
D(t) = $43,200 - ($7,200 × t)
Therefore, the function that can be used to estimate the truck's depreciated value after t years is:
ƒ(t) = $43,200 - ($7,200 × t)
To formulate the function ƒ(t) that can be used to estimate the truck's depreciated value after t years, we need to subtract the depreciated amount per year from the initial value of the truck.
The initial value of the truck is $43,200, and it depreciates at a rate of $7,200 per year. Therefore, for each year t, the depreciated value is given by:
Depreciated value = Initial value - Depreciation per year
ƒ(t) = $43,200 - ($7,200 * t)
So, the function ƒ(t) that can be used to estimate the truck's depreciated value after t years is:
ƒ(t) = $43,200 - $7,200t