The article “Mechanistic-Empirical Design of Bituminous Roads: An Indian Perspective” (A. Das and B. Pandey, Journal of Transportation Engineering, 1999:463–471) presents an equation of the form y = a(1/x1)b(1/x2)c for predicting the number of repetitions for laboratory fatigue failure (y) in terms of the tensile strain at the bottom of the bituminous beam (x1) and the resilient modulus (x2). Transform this equation into a linear model, and express the linear model coefficients in terms of a, b, and c.

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Q: Calculate the least squares estimate of the intercept. (Round your answer to 3 decimal places.)

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A: Given: ∑yi=572∑yi2=23530∑xi=43∑xi2=157.42∑xiyi=1697.80n=14

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A: Given Information: n=14 ∑yi=572, ∑yi2=23530, ∑xi=43, ∑xi2=157.42, ∑xiyi=1697.80

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A: x: compressive strength y: permeability n=14 ∑y=572∑y2=23530∑x=43∑x2=15742

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.