Question

v. math of finance sem a- a
mobile ownership
asset depreciation
the table shows the depreciation for an asset with an initial cost of $16,000
, salvage value of $4,000, and useful life of 4 years
which equation represents the straight-line depreciation from the table?
$d(t) = 4,000 - 3,000t$
$d(t) = 3,000t + 4,000$
$d(t) = 16,000 - 4,000t$
$d(t) = 16,000 - 3,000t$

Explanation:

Step1: Identify the formula for straight - line depreciation

The book value \( D(t) \) of an asset with initial cost \( C \), annual depreciation \( d \), and time \( t \) (in years) is given by the formula \( D(t)=C - dt \).

Step2: Determine the initial cost and annual depreciation

From the problem, the initial cost \( C=\$16,000 \). Looking at the table, the annual depreciation expense is \$3,000 (since for each year, the depreciation expense is \$3,000). So \( d = 3000 \).

Step3: Substitute into the formula

Substituting \( C = 16000 \) and \( d=3000 \) into the formula \( D(t)=C - dt \), we get \( D(t)=16000-3000t \).

We can also verify by plugging in values of \( t \):

• For \( t = 1 \): \( D(1)=16000 - 3000\times1=13000 \), which matches the book value in year 1.
• For \( t = 2 \): \( D(2)=16000 - 3000\times2 = 10000 \), which matches the book value in year 2.
• For \( t = 3 \): \( D(3)=16000 - 3000\times3=7000 \), which matches the book value in year 3.
• For \( t = 4 \): \( D(4)=16000 - 3000\times4 = 4000 \), which matches the salvage value (book value in year 4).

Answer:

\( D(t) = 16,000 - 3,000t \)