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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## This note was uploaded on 02/12/2014 for the course MATH 256 taught by Professor Ericcytrynbaum during the Spring '13 term at UBC.

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