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## Resources

Modeling Scenario

## 1-025-MixingItUp-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: compartment salt tank mixing

47 total view(s), 27 download(s)

## Abstract

Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

## Citation

Researchers should cite this work as follows:

## Description

As an example consider Activity 1 (and there are two other Activities).

At time t = 0 a tank contains Q(0) = 4\$ lb of salt dissolved in 100 gal of water. Water containing 0.25 lb of salt per gallon is entering the tank at a rate of 3 gal/min, and the well-stirred solution leaves the tank at the same rate.

[a)] Build a differential equation for the amount of salt, \$Q(t)\$, in lb in the tank at time t in min. Hint: Keep track of the amount of salt that enters and exits the tank per minute.

[b)] Find an expression for the amount of salt, Q(t), in lb in the tank at time t in min and plot Q(t) vs. t over time interval [0, 200] min.

[c)] Determine when the amount of salt doubles from the original amount in the tank.

[d)] Determine when the amount of salt in the tank is 20 lb.

[e)] Determine when the amount of salt in the tank is 30 lb.

[f)] Determine the maximum amount of salt in the tank and when it occurs.

[g)] Describe the long term behavior of the amount of salt in the tank using accompanying plots to support your description.

## Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

## Comments

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