WEBVTT

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Annual and cumulative traffic. Q0 = 1,000 annual units; g = 0%, 3% and 5%.

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MATHEMATICS · define the relationship and the meaning of each symbol before calculating.

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Q0 = 1,000 annual units; g is an annual growth fraction, not a percentage numeral. Future-year sum excludes year 0. No E80 equivalency factor is assumed.

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INPUT · growth scenarios · read the axis units and the numerical values.

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Q0 = 1,000 annual units; g = 0%, 3% and 5%.

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g = 0%: year 5 = 1,000.00; sum of years 1–5 = 5,000.00 units.

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g = 3%: year 5 = 1,159.27; sum of years 1–5 = 5,468.41 units.

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g = 5%: year 5 = 1,276.28; sum of years 1–5 = 5,801.91 units.

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OUTPUT · five future years · read the axis units and the numerical values.

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At 3%, year 5 is 1,159.27 units, while the five-year sum is 5,468.41. Annual and cumulative quantities are different outputs.

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CALCULATION · substitute the defined inputs; keep units through each intermediate step.

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Year one: 1000 × 1.03 = 1030 annual units

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Year five: 1000 × 1.03⁵ = 1159.274074 annual units

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Geometric sum: 1000 × 1.03 × (1.03⁵ − 1) / 0.03 = 5468.409884 five-year units

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Zero-growth limit: 5 × 1000 = 5000 five-year units

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SENSITIVITY · change one declared input · read the axis units and the numerical values.

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Growth 0%: 5000 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

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Growth 3%: 5468.41 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

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Growth 5%: 5801.91 cumulative units. Five future years; year zero excluded; starting annual quantity 1000.

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Check: Compare the loop and geometric expression, test g = 0, and check the year-one term. Preserve whether the starting input is daily or annual; apply a daily-to-annual conversion only once and document the selected calendar convention.

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ONE ROW · Three percent feels modest until the planning horizon gives it thirty opportunities to compound.

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PARAMETER MAP · 7381 evaluated cells. The colour limits stay fixed across every row.

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Trace one growth-rate row through time before comparing rates. The same base quantity of 1,000 units/year anchors every scenario. The upper rows pull away increasingly with time

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because each increase compounds on the previous quantity. Fractional times draw the mathematical curve; annual reporting uses integer years.

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VALUE LANDSCAPE · Height and colour encode Annual quantity (units/year). This is a graph over the two input axes, not automatically a physical pavement shape.

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Prescribed constant growth scenarios, not a forecast. No daily-to-annual conversion, vehicle classification, directional allocation or E80 factor has been silently added.

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Annual quantities are scenario inputs; E80 factors require an applicable method.