1. ## Depreciation

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

The value $\displaystyle V$ of a machine $\displaystyle t$ years after it is purchased is inversely proportional to the square root of $\displaystyle t+1$. The initial value of the machine is $10,000. Write$\displaystyle V$as a function of$\displaystyle t$then find the rate of depreciation when$\displaystyle t=1$and$\displaystyle t=3$. Any assistance again would be great. 2. The value$\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 $\displaystyle \frac{dV}{dt}$

3. 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}$Thank you very much for replying! I understand a bit of what you wrote, but not all of it -- could you (or someone else) take this a step further and show me how for example I'd write dV/dt and solve down for k? I learn from examples best and I have no examples to follow on problems like this so I would really appreciate a more lay-men's solution (again sorry to be such a pest, it's just I need to see each step in order to fully understand it ) Thanks again! 4. Originally Posted by jimmyp Thank you very much for replying! I understand a bit of what you wrote, but not all of it -- could you (or someone else) take this a step further and show me how for example I'd write dV/dt and solve down for k? I learn from examples best and I have no examples to follow on problems like this so I would really appreciate a more lay-men's solution (again sorry to be such a pest, it's just I need to see each step in order to fully understand it ) Thanks again!$\displaystyle V = k (t + 1)^{-1/2}$. You're expected to know the general rule that if$\displaystyle y = k (ax + b)^n$then$\displaystyle \frac{dy}{dx} = k n a (ax + b)^{n-1}\$.