Question

A tank contains 5000 litres of pure water. Brine (very salty water) that contains 30 grams of salt per litre of water is pumped into the tank at a rate of 25 litres per minute. The concentration of salt water after t minutes (in grams per litre) is C(t) = `(30"t")/(200 + "t")`. What happens to the concentration as t → ∞?

Answer 1

Given the concentration of saltwater after t minutes is C(t) = `(30"t")/(200 + "t")`

 To find the concentration of saltwater after t → ∞

`lim_("t" -> oo) "C"("t") =  lim_("t" -> oo) (30"t")/(200 + "t")`

= `lim_("t" -> oo) (30"t")/("t"(200/"t" + 1))`

= `lim_("t" -> oo) (30"t")/(200/"t" + 1)`

= `30/(0 + 1)`

`lim_("t" -> oo) "C"("t")` = 30