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    Thanks for all the help!
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    You can say dx/dt = -64 - kx

    Separate the variables and integrate both sides. You know when t = 0, x = 2 so you can include that information with your constant.

    Hint: Might be easier if you put your constant of integration in the form "ln a" so it comes out nicely when you rearrange after integrating.
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    (Original post by Ben121)
    You can say dx/dt = -64 - kx

    Separate the variables and integrate both sides. You know when t = 0, x = 2 so you can include that information with your constant.

    Hint: Might be easier if you put your constant of integration in the form "ln a" so it comes out nicely when you rearrange after integrating.
    I don't have a clue how to get that equation.
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    Initially, 2kg of actinium is present and the rate of decay of its mass is 64g/year"...so x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    " Subsequently, t years later when the actinium has a mass xkg, the rate of decrease of mass is proportional to the value of x."
    This means that dx/dt = -kx where k is a positive constant.

    So, -0.064 = -k*2 (when t=0), hence k=0.032.
    Therefore dx/dt = -0.032x.

    Key is to understand the key words: rate = derivative, rate of decay=negative derivative.
    proportional to x mean "constant multiplied by x"
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    (Original post by vc94)
    Initially, 2kg of actinium is present and the rate of decay of its mass is 64g/year"...so x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    " Subsequently, t years later when the actinium has a mass xkg, the rate of decrease of mass is proportional to the value of x."
    This means that dx/dt = -kx where k is a positive constant.

    So, -0.064 = -k*2 (when t=0), hence k=0.032.
    Therefore dx/dt = -0.032x.

    Key is to understand the key words: rate = derivative, rate of decay=negative derivative.
    proportional to x mean "constant multiplied by x"
    Hi there,

    thanks for the help. Sorry but you explain how -k^2 = -0.064 please?
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    We're told that: x=2 and dx/dt = -0.064 (Kg/year) when t=0.

    And since dx/dt = -kx, then substituting we get -0.064 = -k*2 (* means multilply)
 
 
 
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