Question

A business uses straight-line depreciation to determine the value of an automobile over a 6-year period. Suppose the original value (when t=0) is equal to $17,400 and the salvage value (when t=6) is equal to $3000. Write the linear equation that models the value, s, of this automobile at the end of year t.

Answer 1

Answer:
`s=17400-2400t`

Explanation:

Since it is a case of depreciation, there for the rate of change in the price of automobile should be negative.

The rate of change of this linear function is given by:-

`m=\frac{\text{salvage value}-\text{original value}}{t_6-t_0}\\\Rightarrow\ m=(3000-17400)/(6-0)\\\Rightarrow\ m=(-14400)/(6)\\\Rightarrow\ m=-2400`

Thus, the original value of automobile depriciates by rate of $2400 per year.

The the linear equation that models the value, s, of this automobile at the end of year t is given by:-

`s=17400-2400t`