1. ## Depreciation

Another word problem I'm struggling with, any guidance would be great.

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 $t=3$. Any assistance again would be great. 2. The value $V$ of a machine $t$ years after it is purchased is inversely proportional to the square root of $t+1$. $V = \frac{k}{\sqrt{t+1}}$ The initial value of the machine is$10,000.

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

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

solve for $k$ , the constant of proportionality.

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

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

3. Originally Posted by skeeter
The value $V$ of a machine $t$ years after it is purchased is inversely proportional to the square root of $t+1$.

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

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

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

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

solve for $k$ , the constant of proportionality.

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

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

Thank you very much for replying! I understand a bit of what you wrote, but not all of it -- could you (or someone else) take this a step further and show me how for example I'd write dV/dt and solve down for k? I learn from examples best and I have no examples to follow on problems like this so I would really appreciate a more lay-men's solution (again sorry to be such a pest, it's just I need to see each step in order to fully understand it )

Thanks again!

4. Originally Posted by jimmyp
Thank you very much for replying! I understand a bit of what you wrote, but not all of it -- could you (or someone else) take this a step further and show me how for example I'd write dV/dt and solve down for k? I learn from examples best and I have no examples to follow on problems like this so I would really appreciate a more lay-men's solution (again sorry to be such a pest, it's just I need to see each step in order to fully understand it )

Thanks again!
$V = k (t + 1)^{-1/2}$.

You're expected to know the general rule that if $y = k (ax + b)^n$ then $\frac{dy}{dx} = k n a (ax + b)^{n-1}$.