Question

A computer is worth $2000 when it is new. After each year it is worth half what it was the previous year. What will its worth be after 5 years?

Answer 1

It's a simple geometric progression of ratio `r = 1/2`

Explanation:

After the first year, the value will be given by:

`V_1 =$2000*(1/2)=$1000`

In the second:

`V_color(red)(2)=V_1*(1/2)=$2000*color(red)((1/2)*(1/2))=$2000*color(red)((1/2)^2)=500`

In the `n^(th)` year:

`V_color(red)(n)=$2000*(1/2)^color(red)(n)`

So, after 5 years:

`V_5=$2000*(1/2)^5=$2000*(1/32)=($2000)/32=$62.50`