Originally Posted by

**skeeter** **The value $\displaystyle V$ of a machine $\displaystyle t$ years after it is purchased is inversely proportional to the square root of $\displaystyle t+1$. **

$\displaystyle V = \frac{k}{\sqrt{t+1}}$

**The initial value of the machine is $10,000. **

at $\displaystyle t = 0$ , $\displaystyle V = 10000$

$\displaystyle 10000 = \frac{k}{\sqrt{0+1}}$

solve for $\displaystyle k$ , the constant of proportionality.

**Write $\displaystyle V$ as a function of $\displaystyle t$ then find the rate of depreciation when $\displaystyle t=1$ and $\displaystyle t=3$. **

rate of depreciation is $\displaystyle \frac{dV}{dt}$