Abstract

Citation

Researchers should cite this work as follows:

• Brian Winkel (2023). 1-025-MixingItUp-ModelingScenario. SIMIODE, (Version 2.0). QUBES Educational Resources. doi:10.25334/DTJ3-0J43

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Article Context

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.