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Math Help - Depreciation

  1. #1
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    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.
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  2. #2
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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.

    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}
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  3. #3
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    Quote Originally Posted by skeeter View Post
    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!
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  4. #4
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    Quote Originally Posted by jimmyp View Post
    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}.
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