Lecture 3 Notes

3 example freshwater ows into a tank at a rate 2 lmin

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Unformatted text preview: nge in the mass of salt in any short interval of time ∆t ? (A) ∆m ≈ −2 L/min × m(t) / 10 L (B) ∆m ≈ −2 L/min × 100 g/L × ∆t (C) ∆m ≈ −2 L/min × m(t) / 10 L × ∆t (D) ∆m ≈ −2 L/min × m(t) Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( lim t→∞ m(t) )? (a) What is the change in the mass of salt in any short interval of time ∆t ? (A) ∆m ≈ −2 L/min × m(t) / 10 L (B) ∆m ≈ −2 L/min × 100 g/L × ∆t (C) ∆m ≈ −2 L/min × m(t) / 10 L × ∆t (D) ∆m ≈ −2 L/min × m(t) Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( lim t→∞ m(t) )? Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( lim • m(t + ∆t) = m(t) + ∆m so t→∞ m(t) )? Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( lim • m(t + ∆t) = m(t) + ∆m so t→∞ m(t) )? • m(t + ∆t) ≈ m(t) − ∆t × 2 L/min × m(t) / 10 L Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g / L of salt in it and holds 10 L. The tank is well mixed and the mixed water drains out at the same rate as the inflow. (a) Write down an IVP for the mass of salt in the tank as a function of time. (b) What is the limiting mass of salt in the tank ( lim • m(t + ∆t) = m(t) + ∆m t→∞ so m(t) )? • m(t + ∆t) ≈ m(t) − ∆t × 2 L/min × m(t) / 10 L • Rearranging: m(t + ∆t) − m(t) ∆t 1 ≈ − m(t) 5 Modeling (Section 2.3) - Example • Freshwater flows into a tank at a rate 2 L/min. The tank starts with a concentration of 100 g /...
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