You buy a new computer for $2100. The computer decreases by 50% annually. When will the computer have a value of $600?

Answer 1

Hello Rain,

You can use the exponential decay equation to describe the value of the computer over time

V(t) = V_0 * (1-r)^t/t_h where: V_0 is the initial value, v(t) the final value at time t, r is the annual rate of decrease, t_h is the half-life (the time it takes for the value to decrease by 50%) and t is the amount of time elapsed.

Here: V(t) = 600, V_0 = 2100, r = 50% = 0.5, t_h = 1 year (the value decreases by 50% annually), and t is the unknown ("When will the computer have a value of $600?")

So: 600 = 2100 (0.5)^(t/1) ---> 600 = 2100 (0,5)^t ----> (600/2100) = 0.5^t

Take the natural log of both sides: ln(600/2100) = ln 0.5^t -----> ln(600/2100) = t*ln(0.5)

----> t = ln(600/2100) / ln(0.5) = ln (2/7) / ln (0.5)

From here, you can plug it in your calculator and get a numerical value for t.

Cheers.