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Difficulty: EasySequential Processes and State Transitions

A water processing facility processes liquid batches through a three-stage sequential system. The system updates the batch pollutant count (NN) according to the following state transition rules at each stage:

- Stage 1 (Filtration): N1=N0+20N_1 = N_0 + 20
- Stage 2 (Purification): N2=2×N1N_2 = 2 \times N_1
- Stage 3 (Polishing): N3=N2−10N_3 = N_2 - 10

Match each initial pollutant count (N0N_0) on the left to its corresponding final pollutant count (N3N_3) after completing all three stages.

  • Initial Count N0=10N_0 = 10Final Count N3=50N_3 = 50
  • Initial Count N0=25N_0 = 25Final Count N3=80N_3 = 80
  • Initial Count N0=40N_0 = 40Final Count N3=110N_3 = 110

Answer

Initial Count N0=10N_0 = 10 matches Final Count N3=50N_3 = 50; Initial Count N0=25N_0 = 25 matches Final Count N3=80N_3 = 80; Initial Count N0=40N_0 = 40 matches Final Count N3=110N_3 = 110.
Each initial count must be processed sequentially through all three transition rules in exact order: N1=N0+20N_1 = N_0 + 20, then N2=2×N1N_2 = 2 \times N_1, and finally N3=N2−10N_3 = N_2 - 10. Executing this sequence accurately matches N0=10N_0 = 10 to N3=50N_3 = 50, N0=25N_0 = 25 to N3=80N_3 = 80, and N0=40N_0 = 40 to N3=110N_3 = 110.

Step-by-Step Solution

1
Apply Stage 1 transition rule (N1=N0+20N_1 = N_0 + 20) to each initial value.
For N0=10→N1=30N_0 = 10 \rightarrow N_1 = 30; for N0=25→N1=45N_0 = 25 \rightarrow N_1 = 45; for N0=40→N1=60N_0 = 40 \rightarrow N_1 = 60.
Stage 1 adds 20 to the initial state.
2
Apply Stage 2 transition rule (N2=2×N1N_2 = 2 \times N_1) to the intermediate values.
For N1=30→N2=60N_1 = 30 \rightarrow N_2 = 60; for N1=45→N2=90N_1 = 45 \rightarrow N_2 = 90; for N1=60→N2=120N_1 = 60 \rightarrow N_2 = 120.
Stage 2 doubles the state value from Stage 1.
3
Apply Stage 3 transition rule (N3=N2−10N_3 = N_2 - 10) to determine final output states.
For N2=60→N3=50N_2 = 60 \rightarrow N_3 = 50; for N2=90→N3=80N_2 = 90 \rightarrow N_3 = 80; for N2=120→N3=110N_2 = 120 \rightarrow N_3 = 110.
Stage 3 subtracts 10 from the Stage 2 state value.

Key Concept

Sequential processes require evaluating state updates iteratively in strict order, carrying the output of each stage into the next stage.
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Topics

Sequential Processes and State Transitions

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