Redo Problem 12-13 using the average growth factor method.
What will be an ideal response?
First Iteration
Next, use Equation 12.5a to solve the problem. In this step, the movement
between zones is calculated.
TAB = 25 × ((3 + 4) / 2)
TAB = 87.5
TAC = 50 × ((3 + 2) / 2)
TAC = 125
TAD = 25 × ((3 + 1) / 2)
TAD = 50
TBC = 150 × ((4 + 2) / 2)
TBC = 450
TBD = 75 × ((4 + 1) / 2)
TBD = 187.5
TCD = 200 × ((2 + 1) / 2)
TCD = 300
Next, sum the trip ends in each zone and develop the new growth factors.
TA = TAB + TAC + TAD = 87.5 + 125 + 50 = 262.5
TB = TBA + TBC + TBD = 87.5 + 450 + 187.5 = 725
TC = TCA + TCB + TCD = 125 + 450 + 300 = 875
TD = TDA + TDB + TDC = 50 + 187.5 + 300 = 537.5
New growth factor for A = 300 / 262.5 = 1.143
New growth factor for B = 1,000 / 725 = 1.379
New growth factor for C = 800 / 875 = 0.914
New growth factor for D = 300 / 537.5 = 0.558
Second Iteration
Next, use Equation 12.5a to solve the problem. In this step, the movement
between zones is calculated.
TAB = 87.5 × ((1.143 + 1.379) / 2)
TAB = 110.3
TAC = 125 × ((1.143 + 0.914) / 2)
TAC = 128.6
TAD = 50 × ((1.143 + 0.558) / 2)
TAD = 42.5
TBC = 450 × ((1.379 + 0.914) / 2)
TBC = 515.9
TBD = 187.5 × ((1.379 + 0.558) / 2)
TBD = 181.6
TCD = 300 × ((0.914 + 0.558) / 2)
TCD = 220.8
Next, sum the trip ends in each zone and develop the new growth factors.
TA = TAB + TAC + TAD = 110.3 + 128.6 + 42.5 = 281
TB = TBA + TBC + TBD = 110.3 + 515.9 + 181.6 = 808
TC = TCA + TCB + TCD = 128.6 + 515.9 + 220.8 = 865
TD = TDA + TDB + TDC = 42.5 + 181.6 + 220.8 = 445
New growth factor for A = (1.143)(262.5) / 281 = 1.068
New growth factor for B = (1.379)(725) / 808 = 1.238
New growth factor for C = (0.914)(875) / 865 = 0.925
New growth factor for D = (0.558)(537.5) / 445 = 0.674
Additionally, these results could serve as the starting point for a third iteration.
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