Lecture 3 Notes

# The tank is well mixed and the mixed water drains out

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Unformatted text preview: 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) )? dm 1 • What method could you use to solve the ODE = − m(t) ? dt 5 (A) Integrating factors. (B) Separating variables. (C) Just knowing some derivatives. (D) All of these. (E) None of these. 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) )? dm 1 • What method could you use to solve the ODE = − m(t) ? dt 5 (A) Integrating factors. (B) Separating variables. (C) Just knowing some derivatives. (D) All of these. (E) None of these. To think about: what is the most general equation that can be solved using (A) and (B)? 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 • The solution to the IVP is 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 • The solution to the IVP is (A) m(t) = Ce−t/5 (B) m(t) = 100e−t/5 (C) m(t) = 100et/5 (D) m(t) = 1000et/5 (E) m(t) = 1000e−t/5 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 • The solution to the IVP is (A) m(t) = Ce−t/5 (B) m(t) = 100e−t/5 (C) m(t) = 100et/5 (D) m(t) = 1000et/5 (E) m(t) = 1000e−t/5 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 • The s...
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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 The University of British Columbia.

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