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?

1 Answer
Jan 1, 2016

Answer:

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#