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# Last minute P3 help watch

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1. I'm having difficulty interpreting differential equations in essay form. Eg:

A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

Can someone please talk me through it?
2. (Original post by Zapsta)
I'm having difficulty interpreting differential equations in essay form. Eg:

A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

Can someone please talk me through it?
Sack that, I swear if that comes up in the exam I'm done for, I really dislike differential equations.
3. (Original post by Zapsta)
I'm having difficulty interpreting differential equations in essay form. Eg:

A tank contains a solution of salt in water. Initially the tank contains 1000 l of water with 10 kg of salt dissolved in it. The mixture is poured off at a rate of 20 l per min, and simultaneously pure water is added at a rate of 20 l per min. All the time the tank is stirred to keep the mixture uniform. Find the mass of the salt in the tank after 5 mins. The tank must be topped up by adding more salt when the mass of the salt in the tank falls to 5 kg; after how many mins will it need topping up?

Can someone please talk me through it?
This is probably too late but anyway. I think that the rate of decrease of the amount of salt is proportional to the amount of salt in the tank. So,

dS/dt = -kS

You can then solve this and use the initial conditions: when t=0, S=10 but also to find k we use the fact that after one minute the amount of salt should be 9.8 kg; that is, when t=1, S=9.8. I obtain the relation

S = 10(0.98)^t

Can anyone verify this?

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