Lecture 3 Notes

Answer to b lim mt 0 t modeling section 23 example

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Unformatted text preview: olution 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) )? Answer to (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 (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) )? Answer to (b)? lim m(t) = 0 t→∞ Modeling (Section 2.3) - Example • Saltwater with a concentration of 200 g/L flows into a tank at a rate 2 L/min. The tank starts with no 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? Modeling (Section 2.3) - Example • Saltwater with a concentration of 200 g/L flows into a tank at a rate 2 L/min. The tank starts with no 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? (a) The IVP is (A) m’ = 200 - 2m, m(0) = 0 (B) m’ = 400 - 2m, m(0) = 200 (C) m’ = 400 - m/5, m(0) = 0 (D) m’ = 200 - m/5, m(0) = 0 (E) m’ = 400 - m/5, m(0) = 200 Modeling (Section 2.3) - Example • Saltwater with a concentration of 200 g/L flows into a tank at a rate 2 L/min. The tank starts with no 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? (a) The IVP is (A) m’ = 200 - 2m, m(0) = 0 (B) m’ = 400 - 2m, m(0) = 200 (C) m’ = 400 - m/5, m(0) = 0 (D) m’ = 200 - m/5, m(0) = 0 (E) m’ = 400 - m/5, m(0) = 200 Modeling (Section 2.3) - Example • Saltwater with a concentration of 200 g/L flows into a tank at a rate 2 L/min. The tank starts with no 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? Modeling (Section 2.3) - Example • Saltwater with a concentration of 200 g/L flows into a tank at a rate 2 L/min. The tank starts with no 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...
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