Question

suppose a business purchases equipment for $11,000 and depreciates it over 5 years with the straight - line method until it reaches its salvage value of $1000 (see the figure below). assuming that the depreciation can be for any part of a year, answer the questions to the right. (a) write an equation that represents the depreciated value v as a function of the years t. (do not factor.) (b) write an inequality using t as the variable that indicates that the depreciated value v of the equipment is less than $5000. (do not simplify.) (c) write an inequality that describes the time t during which the depreciated value is at least half of the original value. (do not simplify.)

Explanation:

Step1: Find annual depreciation

Annual depreciation = $\frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Useful Life}} = \frac{11000 - 1000}{5} = 2000$

Step2: Write depreciation equation

Depreciated value $V$ = Initial cost - (Annual depreciation $\times$ time $t$)
$V = 11000 - 2000t$

Step3: Set up inequality for part (b)

Set $V < 5000$, substitute $V$:
$11000 - 2000t < 5000$

Step4: Find half original value, set inequality

Half original value = $\frac{11000}{2} = 5500$. Set $V \geq 5500$:
$11000 - 2000t \geq 5500$

Answer:

(a) $V = 11000 - 2000t$
(b) $11000 - 2000t < 5000$
(c) $11000 - 2000t \geq 5500$