Question

A company buys a machine for $225,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n) =

Answer 1

`V(n) =225000*0.7^n`

Explanation:

In this problem we are expected to model the depreciated value of the machine after some years of purchase (n years)

initial value of the machine is $225,000

after a year it reduces by 30%

Therefore the new value is now 70% of the initial value

`= 225000*0.7= 157,500`

= $157,500

After another year it reduces by 30%

Hence the new value is

`=225000*0.7^2\\\=225000*0.49\\\\\=110250`

= $110250

that after n years the value will be

`V(n) =225000*0.7^n`