ANSWER
1 year and 10 months or 1.8 years
EXPLANATION
We have that the price of the new computer is $2100 and it decreases by 50% annually.
This means it is a compound decrement.
So, we can apply the formula:
[tex]A=P(1-R)^t[/tex]where A = price after t years
P = initial price
R = rate of decrease
t = amount of years
Therefore, we have that:
A = $600
P = $2100
R = 50%
Therefore, we need to find t:
[tex]\begin{gathered} 600\text{ = 2100(1 - }\frac{50}{100})^t \\ \frac{600}{2100}=(1-0.5)^t \\ 0.2857=0.5^t \\ \text{ Find the logarithm of both sides:} \\ \log (0.2857)=log(0.5)^t\text{ = t }\cdot\text{log0.5} \\ -0.5441=\text{ t }\cdot\text{ (-0.301)} \\ t\text{ = }\frac{-0.5441}{-0.301} \\ t\text{ = 1.8 years or 1 year and 10 months} \end{gathered}[/tex]The computer will have a value of $600 after 1 year and 10 months.