Differential equation A Level Question help? Watch

Sakura-Sama
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The number of customers at an ice cream parlour decreases after the end of the summer holidays. The rate of change of the decrease can be modelled by the differential equation dC/dt =-kCt(k>0) where c is the number of customers per week, t is the nunber of weeks after the end of the holidays, and k is a constant.
At the end of the holidays, the ice cream parlour had 3600 customers per week. Use this information to solve the differential equation giving your answer as a formula for C in terms of k and t.

So i used the differential equation and got (-1/k)lnC = 1/2t^2
I assumed t as 1 and C as 3600 and I got k as a negative constant so I thinj I'm doing something wrong.
Help is much appreciated thank you!
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Notnek
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(Original post by Sakura-Sama)
The number of customers at an ice cream parlour decreases after the end of the summer holidays. The rate of change of the decrease can be modelled by the differential equation dC/dt =-kCt(k>0) where c is the number of customers per week, t is the nunber of weeks after the end of the holidays, and k is a constant.
At the end of the holidays, the ice cream parlour had 3600 customers per week. Use this information to solve the differential equation giving your answer as a formula for C in terms of k and t.

So i used the differential equation and got (-1/k)lnC = 1/2t^2
I assumed t as 1 and C as 3600 and I got k as a negative constant so I thinj I'm doing something wrong.
Help is much appreciated thank you!
You forgot the constant of integration - this constant isn't k. You need to leave your final answer in terms of k and t.
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Sakura-Sama
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(Original post by Notnek)
You forgot the constant of integration - this constant isn't k. You need to leave your final answer in terms of k and t.
Sorry I'm afraid I don't understand.
Are you saying that there needs to be a c as well as a k?
We need to substitute in 3600 and as a result t=1 as it states 'end of the holidays', all to find k?
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Notnek
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(Original post by Sakura-Sama)
Sorry I'm afraid I don't understand.
Are you saying that there needs to be a c as well as a k?
We need to substitute in 3600 and as a result t=1 as it states 'end of the holidays', all to find k?
There's no way of finding k in this question so don't worry about it. If you solve the DE you should get

(-1/k)lnC = 1/2t^2 + D

where D is the constant of integration (I've avoided C for obvious reasons).

Now you need to plug in the initial conditions to find D in terms of k. Your final answer will have C's t's and k's in it.
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ghostwalker
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(Original post by Sakura-Sama)
I assumed t as 1 and C as 3600
I would have thought c=3600 when t=0, since c=3600 AT the end of the holidays, and t is the number of weeks AFTER the end of the holidays.
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the bear
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agree with ghostwalker.... c = 3600 when t = 0
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begbie68
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ditto
(Original post by the bear)
agree with ghostwalker.... c = 3600 when t = 0
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