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# C4 Differential Equations Help Please. :) watch

1. Thanks for all the help!
2. 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.
3. (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.
4. 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"
5. (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?
6. 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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