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 May 31st, 2009, 08:43 PM #1 Newbie   Joined: May 2009 Posts: 5 Thanks: 0 Word problem Hello, I need some help with this word problem: The value V of a machine t years after it is purchased is inversely proportional to the square root of t+1. The initial value of the machine is $10,000. Write V as a function of t then find the rate of depreciation when t=1 and t=3. Can someone solve down for me and show me what they've done along the way so I can understand it? Thanks a lot for reading.  June 1st, 2009, 01:52 AM #2 Senior Member Joined: Dec 2008 Posts: 251 Thanks: 0 Re: Word problem To say that $V(t)$ is inversely proportional to $\sqrt{t\,+\,1}$ is to say that $V(t)\,=\,\frac{k}{\sqrt{t\,+\,1}$ for some constant $k$. Differentiating, we obtain $\begin{eqnarray*} V'(t) &=& \frac{d}{dt}\left(\frac{k}{\sqrt{t\,+\,1}}\right)\ \ &=& k\frac{d}{dt}(t\,+\,1)^{-\frac{1}{2}}\\ &=& -\frac{1}{2}k(t\,+\,1)^{-\frac{3}{2}}.\mbox{ (Power Rule)}\\ \end{eqnarray*}$ Now all that is left is to find the rates of depreciation $-V'(1)$ and $-V'(3)$. June 1st, 2009, 05:06 AM #3 Senior Member Joined: Mar 2009 Posts: 318 Thanks: 0 Quote:  Originally Posted by hemidol The value V of a machine t years after it is purchased is inversely proportional to the square root of t+1. The initial value of the machine is$10,000. Write V as a function of t then find the rate of depreciation when t=1 and t=3.
The first part is something they were supposed to have taught you back in algebra; namely, setting up the variation equation. To learn how the previous poster came up with the equation, try here.

Please study at least two lessons from the link. You will need to know this!

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### the value v of a machine t years after it is purchased is inversely proportional to the square root of t 1. the initial value of the machine is \$10,000

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