Respuesta :
Explanation:
The concentration of salt after t minutes is given by :
[tex]C(t)=\dfrac{40t}{360+t}[/tex]
A tank contains 9000 L of pure water. Brine that contains 40 g of salt per liter of water is pumped into the tank at a rate of 25 L/min.
We need to find the concentration approach at [tex]t\rightarrow \infty[/tex]
So, [tex]\lim_{t \to \infty}C(t)=\dfrac{40t}{360+t}[/tex]
[tex]\lim_{t \to \infty}C(t)=\dfrac{40}{\dfrac{360}{t}+1}[/tex]
Put [tex]t=\infty[/tex]
[tex]\lim_{t \to \infty}C(t)=\dfrac{40}{\dfrac{360}{\infty}+1}[/tex]
Since, [tex]\dfrac{360}{\infty}=0[/tex]
C(t) = 40 g/L
So, at [tex]t\rightarrow \infty[/tex] the concentration approaches to 40 g/L. Hence, this is the required solution.
