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 1150 dollar
refrigerator depreciates completely in 9 years, find a formula for its value as a function of time, x, in years.
value =
dollars

Answer 1

Depreciation implies the rate at which an asset is written off per year. So that the required formula is: value = $1150 - $127.78x.

Depreciation of an asset is a simple way of writing off the asset with respect to its life span. Using straight line method, the formula for determining depreciation is:

Depreciation = $\frac{Cost of asset - Residual value}{Time(years)}$

The residual value is the cost of the asset after its useful life.

Thus, in the given question, residual value of the asset = 0

So that,

Depreciation = $\frac{Cost of asset}{Time}$

                      = $\frac{1150}{9}$

Depreciation = 127.78

Thus, the depreciation of the asset is $127.78 per year.

Therefore since the asset depreciates by 127.78 every year, then the formula for its value as a function of time in years is:

Value = $1150 - $127.78x

where x is in years.

The required formula for the value is $1150 - $127.78x

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