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Thread: limit with g/L

  1. #1
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    limit with g/L

    A tank contains 3000 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. The concentration of salt after t minutes (in grams per liter) is given by the function below. As t , what does the concentration approach?



    you have to find g/L
    so i thought you plug in 25 for t, but when i did that i just got 3000, which is wrong
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  2. #2
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    Quote Originally Posted by kyleu03 View Post
    A tank contains 3000 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. The concentration of salt after t minutes (in grams per liter) is given by the function below. As t , what does the concentration approach?



    you have to find g/L
    so i thought you plug in 25 for t, but when i did that i just got 3000, which is wrong
    I may be reading this wrong, and I probably am because I'm really tired, but...

    It seems to me that the only relevant info here is the given function. To find $\displaystyle C(t)$ as $\displaystyle t\to\infty$ simply divide numerator and denominator by $\displaystyle t$. Then the limit becomes obvious.

    $\displaystyle \lim_{t\to\infty}\frac{25t}{120+t}=\lim_{t\to\inft y}\frac{25}{\frac{120}{t}+1}=25g/L$
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