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[-/2 Points] A tank contains 1,000 L of pure water. Brine that contains 25 g of salt per liter of water is...

17. [-/2 Points]
A tank contains 1,000 L of pure water. Brine that contains 25 g of salt per liter of water is pumped into the tank at a rate of 25 L/min.
(a) Find the concentration of salt, after t minutes (in g/L).
C(t) = ____ g/L
(b) What happens to the concentration (in g/L) as t → ∞?
____ g/L

Answer

  1. The concentration of salt after t minutes can be found by considering the rate of salt being added. The rate of salt added is 25 g/L * 25 L/min = 625 g/min. The volume of the tank increases by 25 L/min, so after t minutes, the volume is 1000 + 25t L. The concentration C(t) is given by:

    C(t) = \( \frac{625t}{1000 + 25t} \) g/L

  2. As t → ∞, the concentration approaches the concentration of the incoming brine, which is 25 g/L. Therefore:

    25 g/L

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