Need help in solving this problem. Section is under limits at infinity, horizontal asymptotes...

AA tank contains 5000L of pure water. Brine that contains 30g of salt per liter of water is pumped into the tank at a rate of 25L/min. Show that the concentration of salt after t minutes (in grams per liter) is

C(t)+ 30t/200+t

Bwhat happens to the concentration as t--> infinity?

Question

22-11-2016
Mathematics

Answered

Need help in solving this problem. Section is under limits at infinity, horizontal asymptotes...

AA tank contains 5000L of pure water. Brine that contains 30g of salt per liter of water is pumped into the tank at a rate of 25L/min. Show that the concentration of salt after t minutes (in grams per liter) is

C(t)+ 30t/200+t

Bwhat happens to the concentration as t--> infinity?

Verified Answer :

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Anonymous Anonymous · Answer 1 · 2016-11-25T07:51:23-05:00

(a) you can show the concentration by:

amount of salt / amount of water

amount of salt

= 30g / L

= [ 30 25g ] / [ 25L ] , 25L = 1 min

= [ 30 25g ] / min

amount of water

= 5000 + 25t

[ 30 25t ] / [ 5000 + 25t ]

= [ 30 25t ] / 25[ 200 + t ]

= 30t / [ 200 + t ] yeah

(b)

lim t->∞ [ 30t / ( 200 + t ) ]

= lim t->∞ [ ( (1 / t) 30t ) / ( (1 / t) * ( 200 + t ) ) ]

= lim t->∞ [ 30 / ( (200 / t) + 1 ) ]

= 30 / ( (200 / ∞) + 1 )

= 30 / 1

= 30

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