At t = 0, a tank of volume 300 L is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exits at the same rate. Let c1(t) be the salt concentration at time t . (a) Find a differential equation satisfied by c1(t) Hint: Find the differential equation for the quantity of salt y(t), and observe that c1(t) = y(t)/100. (b) Find the salt concentration c1(t) in the tank as a function of time.
At t = 0, a tank of volume 300 L is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exits at the same rate. Let c1(t) be the salt concentration at time t . (a) Find a differential equation satisfied by c1(t) Hint: Find the differential equation for the quantity of salt y(t), and observe that c1(t) = y(t)/100. (b) Find the salt concentration c1(t) in the tank as a function of time.
At t = 0, a tank of volume 300 L is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exits at the same rate. Let c1(t) be the salt concentration at time t . (a) Find a differential equation satisfied by c1(t) Hint: Find the differential equation for the quantity of salt y(t), and observe that c1(t) = y(t)/100. (b) Find the salt concentration c1(t) in the tank as a function of time.
At t = 0, a tank of volume 300 L is filled with 100 L of water containing salt at a concentration of 8 g/L. Fresh water flows in at a rate of 40 L/min, mixes instantaneously, and exits at the same rate. Let c1(t) be the salt concentration at time t . (a) Find a differential equation satisfied by c1(t) Hint: Find the differential equation for the quantity of salt y(t), and observe that c1(t) = y(t)/100. (b) Find the salt concentration c1(t) in the tank as a function of time.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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