Traffic growth for highway design: If the last traffic census recorded P vehicles per day, the annual growth rate is r (fraction per year), and n years have elapsed since the last count, what is the design traffic A (vehicles/day)?

Introduction / Context:
Forecasting design traffic is a key step in pavement and geometric design. A common method assumes compound annual growth from a base traffic count to estimate the current or design-year average daily traffic.

Given Data / Assumptions:

• Base count P = vehicles/day at last census.
• Annual growth rate r (e.g., 0.06 for 6%).
• Elapsed time n years since the census.
• Uniform compound growth, no disruptive step changes.

Concept / Approach:
Compound growth increases traffic multiplicatively each year. Therefore, future traffic equals the base multiplied by the compounding factor repeated n times.

Step-by-Step Solution:

Verification / Alternative check:
For small r, a linear approximation P(1 + n r) is sometimes used for quick checks; however, design uses the compound expression.

Why Other Options Are Wrong:
(b) implies decline; (c) and (d) are nonstandard exponents unrelated to elapsed years.

Common Pitfalls:
Using percentage (e.g., 6) instead of fraction (0.06) in (1 + r); ignoring compounding for multi-year projections.

Final Answer:
P (1 + r)^n