A tank contains 8000 L of pure water. Brine that contains 35 g of salt per liter of water is pumped into the tank at a rate of 25 L/min. The concentration of salt after t minutes (in grams per liter) is C(t) = 35t 320 + t . As t → [infinity], what does the concentration approach?

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valetta valetta · Answer 1 · 2020-04-09T09:16:52+02:00

Answer:

The concentration of salt in the tank approaches [tex]35 \mathrm{g} / \mathrm{L},[/tex]

Step-by-step explanation:

Data provide in the question:

Water contained in the tank = 8000 L

Salt per litre contained in Brine = 35 g/L

Rate of pumping water into the tank = 25 L/min

Concentration of salt [tex]\lim _{t \rightarrow \infty} C(t)=\lim _{t \rightarrow \infty} \frac{35 t}{320+t}[/tex]

Now,

Dividing both numerator and denominator by [tex]t[/tex], we have

[tex]\lim _{t \rightarrow \infty} \frac{\frac{1}{t} 35 t}{\frac{1}{t}(320+t)}=\lim _{t \rightarrow \infty} \frac{35}{\frac{320}{t}+1}=35[/tex]

Here,

The concentration of salt in the tank approaches [tex]35 \mathrm{g} / \mathrm{L},[/tex]