The Miles Equation

Question

The number of miles s of roads cleared of snow is approximated by the model

s(ℎ) = 25 − ((13ln (h/12))/ln(3))

,-(+) , 2 ≤ ℎ ≤ 15 where h is the depth of snow in inches. Use the model to

find s when h = 9 inches. (Show work and round to tenths)

Answer 1

I'll solve this step-by-step by substituting h = 9 into the Miles Equation.

Given:

1. s(h) = 25 − (13ln(h/12))/ln(3)
2. h = 9 inches

Solution:

Step 1: Substitute h = 9 into the equation s(9) = 25 − (13ln(9/12))/ln(3)

Step 2: Simplify the fraction inside the natural log s(9) = 25 − (13ln(0.75))/ln(3)

Step 3: Calculate ln(0.75) ln(0.75) ≈ -0.2877

Step 4: Calculate ln(3) ln(3) ≈ 1.0986

Step 5: Calculate the fraction (13ln(0.75))/ln(3) = (13 × (-0.2877))/1.0986 = -3.7401/1.0986 ≈ -3.4041

Step 6: Complete the calculation s(9) = 25 − (-3.4041) s(9) = 25 + 3.4041 s(9) = 28.4041

Step 7: Round to tenths s(9) ≈ 28.4 miles

Answer: When the snow depth is 9 inches, approximately 28.4 miles of roads can be cleared.