IVP: Initial-Value-Problem 1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second,3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept wellmixed at all times.(a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation.(b) Solve the IVP from part (a).2. Now consider the same model as in question 1, but with a "salt buffer" involved. This buffer will add saltif the concentration is below 1kg/L and will remove salt if the concentration is above 1kg/L.(a) Propose an ODE that would model the salt content in the tank and explain it. If you are using anyparameters for unknowns, explain what they mean.Note that there are many correct ways to set this up.(b) Without solving the ODE, answer the following: If at a certain moment there is a salt concentration of1kg/L in the tank, and taking into account all effects, is the amount of salt increasing or decreasingat that moment?

1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second, 3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept well mixed at all times. (a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation. (b) Solve the IVP from part (a).

1. Consider a 100L tank containing 50L of salt water with a concentration of 1kg/L. Suppose that each second, 3L of pure water flows into the tank and 2L of the mixture flows out of the tank. The tank is kept well mixed at all times. (a) Write an IVP that governs the salt content in the tank. Make sure to explain your equation. (b) Solve the IVP from part (a).

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Solve the initial value problem by the linear or separable method
Show all step by step solution. Find P(6) and P(5) for a binomial experiment. Explain your work.
The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the value of the y-intercept (a) estimated in the linear prediction equation provided above (= 22-1.3x)? Also, interpret the y-intercept. y-intercept: Interpretation of y-intercept:
dx 3. S e2xV2e-3x_e-4x