It is estimated that t years from now, the value of a small piece of land, V(t), will be increasing at a rate of 1.6t^3/(0.2t^4+8100)^(1/2)dollars per year. The land is currently worth $420. Find V(t) and also find the value of the land after 10 years to the nearest cent.

Answer 1

dv/dt = 1.6t^3/√(0.2t^4+8100)
Let u = 0.2t^4+8100
du = 0.8t^3 dt

Now you have

dv/dt = 2du/√u
v(t) = 4√u + c
= 4√(0.2t^4+8100) + c

Now plug in your numbers to find c, and then find v(10).