A piece of furniture is worth $2500. Its value ,V, is depreciating at a rate proportional to the square root of the time,t, in years. The piece of furniture will be worth $1600 in 4 years. How long will it take for it to be worth $1280?
dv/dt = -k√t
v = -2k/3 t^(3/2) + c
since v(0) = 2500, c = 2500
v = 2500 - 2k/3 t^(3/2)
since v(4) = 1600, c - 2/3 (8)k = 1600
2500 - 16/3 k = 1600
k = 168.75
so, v = 2500 - 112.5 t^(3/2)
Now just find t such that v=1280