A manufacturer buys $280,000 worth of machinery that depreciates linearly so that its trade-in value after 10 years will be $30,000. Express the value of the machinery (V) as a function of its age (t).
The slope of the line is (30000-280000)/10 = -25000
So,
V(t) = 280,000 - 25,000t
To express the value of the machinery as a function of its age, we need to determine the rate at which it depreciates linearly.
We can use the information given to find the rate of depreciation per year. The machinery depreciates from $280,000 to $30,000 over a period of 10 years.
The depreciation per year can be calculated as follows:
Depreciation per year = (Initial value - Final value) / Number of years
Depreciation per year = ($280,000 - $30,000) / 10
Depreciation per year = $250,000 / 10
Depreciation per year = $25,000
Now that we know the rate of depreciation per year, we can express the value of the machinery at any given age (t) using the linear depreciation formula:
V(t) = Initial value - (Depreciation per year * t)
Where:
V(t) is the value of the machinery at age t
Initial value is the value of the machinery when it was brand new ($280,000 in this case)
Depreciation per year is the rate at which the machinery depreciates ($25,000 in this case)
t is the age of the machinery in years
Therefore, the function that expresses the value of the machinery (V) as a function of its age (t) is:
V(t) = $280,000 - ($25,000 * t)