Question

For tax purposes, you may have to report the value of your assets, such as cars or refrigerators. The value you report drops with time. Straight-line depreciation'' assumes that the value is a linear function of time. If a 1600 dollar refrigerator depreciates completely in 15 years, find a formula for its value as a function of time, x, in years.

Answer 1

Answer:

y=-107 x+1,600, where y is the value of the refrigerator in x years, and x is the number of years.

Explanation:

Straight line depreciation is a method of asset valuation where the fixed asset is assumed to undergo constant depreciation per unit time. This means that the change in value during a given period is constant, where if you plot a value of asset value on the vertical axis against time, x in years you get a linear relationship thus the name straight-line depreciation.

The depreciation of the refrigerator in our case can be expressed as;

{(I-F)/x}=k

where;

I=initial value of refrigerator

F=final value of refrigerator

x=time interval

k=constant of proportionality

{(Initial value-final value)/time interval}=K

In our case;

I=1,600

F=0

x=15 years

replacing;

{(1,600-0)/15}=k

k=1,600/15=107

Express the equation where;

Initial value=1,600

value after x years=y

k=107

time=x

replacing;

(1,600-y)/x=107

1,600-y=107 x

y=-107 x+1,600

The formula is;

y=-107 x+1,600, where y is the value of the refrigerator in x years, and x is the number of years.