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Learn through experiments

An efficient replacement has an upfront cost

When does lower operating impact offset manufacturing and increased use?

Entering midway? Revisit Compare the trip, not the empty seat for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original synthetic scenario. An existing device uses 40 impact units per period. A replacement has an upfront impact, lower impact per use, and a possible increase in use.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

At an upfront impact of 120 and a saving of 10 per period, how long until replacement matches keeping the old device?

3 · Experiment

Change one thing. Inspect what happens.

  1. Compare horizons before, at and after twelve periods at defaults.
  2. Add 20% extra use and recompute the net saving per period.
  3. Find a usage increase where replacement never pays back a positive upfront impact.
  4. State a service-normalized comparison and explain whether increased use creates additional value or avoidable demand.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Keep existing total480 impact units
Replace total480 impact units
Replacement minus keeping0 impact units
Net operating saving per period10 impact units

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
0480
  • Keep existing (impact units)480
    Keep existing (impact units): 480Horizontal bar from zero to 480, on the shared zero to 480 numeric axis.
  • Replace (impact units)480
    Replace (impact units): 480Horizontal bar from zero to 480, on the shared zero to 480 numeric axis.

Follow the calculation

  1. Existing operation: 40 × 12 = 480 impact units.
  2. Replacement rate before usage change = 40 − 10 = 30.
  3. Replacement = upfront 120 + 30 × 12 × (1 + 0) = 480.
  4. Net saving each period = 40 − 30 × 1 = 10.
  5. Break-even horizon = 120 / 10 = 12.000 periods under constant assumptions.

A lower per-use footprint can be offset by manufacturing impact and increased use. State the time horizon and service delivered when comparing options.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

What the experiment explains

Original synthetic scenario. An existing device uses 40 impact units per period. A replacement has an upfront impact, lower impact per use, and a possible increase in use.

Lifecycle comparison includes one-time impact and operating impact over a declared horizon. Ignoring either can change the decision.

At defaults, keeping uses 40×12=480 units. Replacing uses 120+30×12=480. The equal-use break-even is 120/10=12 periods.

With 20% extra use, replacement operation becomes 30×1.2=36 per period, so net savings shrink to four and break-even moves to 30 periods. A lower per-use impact need not mean lower total impact.

Read the relationship

Keep = 40h. Replace = E + (40−s)h(1+r). h is periods, E upfront impact, s equal-use saving, r fractional extra use.

Inspect the evidence

The numerical trace is recalculated from your current settings. Compare a controlled pair of trials before changing several inputs together. Inspect intermediate quantities as well as final metrics; state which assumptions make the comparison meaningful.

Boundaries of the model

  • Generic invented impact units, constant rates and no discounting, disposal or maintenance.
  • Extra use changes the service delivered; interpret totals alongside that difference.

Return to the environment and sustainability course and project to connect this mechanism to the broader investigation.

5 · Apply

Try a fresh case

A fresh replacement has upfront impact 60, old operation 20 per period and new operation 15, with equal use. After how many periods do totals match?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Plot both cumulative totals and label their intersection.

College investigation

Add uncertain lifetime and maintenance scenarios without mixing incompatible impact categories.

Workplace investigation

Write a replacement decision brief separating service demand, manufacturing evidence and operating measurements.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.