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notka56 [123]
3 years ago
5

A tank contains 9000 L of pure water. Brine that contains 20 g of salt per liter of water is pumped into the tank at a rate of 2

5 L/min. The concentration of salt after t minutes (in grams per liter) is C(t) = 20t/360+t As t → [infinity], what does the concentration approach?

Chemistry
1 answer:
geniusboy [140]3 years ago
6 0

Answer:

20 g/L

Explanation:

To know what happens with the concentration, we must calcute the limit of the function where t → ∞. The limit is the value that the function approach when t intend to a value. So:

\lim_{t \to \infty} C(t) =  \lim_{t \to \infty}\frac{20t}{360 + t}

Dividing both for "t"

\lim_{t \to \infty} C(t) =  \lim_{t\to \infty} \frac{\frac{1}{t}20t }{\frac{1}{t}(360 + t) }

\lim_{t \to \infty} \frac{20}{\frac{360}{t} + 1 }

The limit of 1/t when t intend to infity is 0, which is demonstrated in the graph below, so:

\lim_{t\to \infty} 20 = 20

The concentration will approach 20 g/L.

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