Suppose a business purchases equipment for ​$17 comma 000 and depreciates it over 5 years with the​ straight-line method until it reaches its salvage value of ​$2000 ​(see the figure​ below). Assuming that the depreciation can be for any part of a​ year, answer the questions to the right.

Question

Suppose a business purchases equipment for ​$17 comma 000 and depreciates it over 5 years with the​ straight-line method until it reaches its salvage value of ​$2000 ​(see the figure​ below). Assuming that the depreciation can be for any part of a​ year, answer the questions to the right.
Suppose a business purchases equipment for ​$17 comma 000 and depreciates it over 5 years with the​ straight-line method until it reaches its salvage value of ​$2000 ​(see the figure​ below). Assuming that the depreciation can be for any part of a​ year, answer the questions to the right.
Write an inequality using t as the variable that indicates that the depreciated value V of the equipment is less than ​$8000.

Answer 1

To compute the depreciated value of the equipment $V$ using the straight-line depreciation method, you can use the following formula:

$$V=C-D\cdot t$$

Where:

• $C$ is the initial cost of the equipment ($17,000).
• $D$ is the annual depreciation expense.
• $t$ is the number of years that have passed.

First, we need to calculate the annual depreciation expense $D$:

$$D=\frac{C-\text{salvage value}}{\text{useful life}}=\frac{17000-2000}{5}=\frac{15000}{5}=3000$$

So, the annual depreciation expense $D$ is $3,000.

Now, we can express the depreciated value $V$ after $t$ years as:

$$V=17000-3000\cdot t$$

We want to find the inequality that indicates that $V$ is less than $8,000:

$$17000-3000t<8000$$

Now, we can solve this inequality step-by-step:

1. Subtract 17000 from both sides:

$$-3000t<8000-17000$$

$$-3000t<-9000$$

2. Divide by -3000 (remember to flip the inequality when dividing by a negative number):

$$t>\frac{-9000}{-3000}$$

$$t>3$$

Therefore, the inequality that indicates the depreciated value $V$ of the equipment is less than $8,000 is:

$$t>3$$

This means that the equipment will have a depreciated value of less than $8,000 after more than 3 years.