Need in solving this problem. section is under limits at infinity, horizontal

(a) a 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
(b) what happens to the concentration as t--> infinity?

 (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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