Susie purchased a laptop computer for $2000 at the beginning of the year in 2008,the value of the computer decreased by 20% each year. Susie wants to purchase a new laptop computer when the value of hers falls below $500. When will Susie be able to purchase a new laptop?

so you are solving

2000(.8)^n = 500
.8^n = 500/2000 = .25
take log of both sides

log .8^n = log .25
n log .8 = log .25
n = log .25/log .8 = appr 6.2 years

To determine when Susie will be able to purchase a new laptop, we need to find out in which year the value of her current laptop falls below $500.

Since the value of the laptop decreases by 20% each year, we can compute the value of the laptop for each year using the following formula:

Value = Initial Value - (rate of decrease * Initial Value)

Let's calculate the value of the laptop for each year:

Year 1:
Value = $2000 - (20% * $2000) = $2000 - $400 = $1600

Year 2:
Value = $1600 - (20% * $1600) = $1600 - $320 = $1280

Year 3:
Value = $1280 - (20% * $1280) = $1280 - $256 = $1024

Year 4:
Value = $1024 - (20% * $1024) = $1024 - $204.8 = $819.2

Year 5:
Value = $819.2 - (20% * $819.2) = $819.2 - $163.84 = $655.36

Based on the calculations, the value of Susie's current laptop will fall below $500 in the fifth year. Therefore, she will be able to purchase a new laptop in the fifth year.