Copy of Tutorial 1_trend curves

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a = 8 b= 5 r= 0.9 Linear: Constant Increase and Declining Growth Rate Demand = a + b Time t 1 2 3 4 5 6 7 8 (demand) = a + b Time 13.000 18.000 23.000 28.000 33.000 38.000 43.000 48.000 %change 38.5% 27.8% 21.7% 17.9% 15.2% 13.2% 11.6% Log - Linear: Constant growth rate exp(1) = 2.718 ln(Demand) = a + b/100 Time Demand = Exp(a + b/100 Time) t 1 2 3 4 5 6 7 8 Ln(demand) = a + (b/100) (t) 8.180 8.100 8.150 8.200 8.250 8.300 8.350 8.400 Demand = Exp(a + b/100 Time) 3569 3294 3463 3641 3828 4024 4230 4447 %change -7.7% 5.1% 5.1% 5.1% 5.1% 5.1% 5.1% Log-Log ln(Demand) = ln(a) + r log(t) Demand = Exp(a t^r) t 1 2 3 4 5 6 7 8 Log(demand) = ln(a) + r log(t) 2.079 2.703 3.068 3.327 3.528 3.692 3.831 3.951 Demand 8 15 22 28 34 40 46 52 %change 86.6% 44.0% 29.6% 22.2% 17.8% 14.9% 12.8% Logistic - Exponential Decay Demand = (a + br^t) Lower Assymptote = a t 1 2 3 4 5 6 7 8 Demand 12.500 12.050 11.645 11.281 10.952 10.657 10.391 10.152 %change -3.6% -3.4% -3.1% -2.9% -2.7% -2.5% -2.3% 0.041230202 0.125 Inverse Time - Continues Decay Demand = a + b /Time Lower Assymptote = a t 10 11 12 13 14 15 16 17 (demand) = a + b/Time 8.500 8.455 8.417 8.385 8.357 8.333 8.313 8.294
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Unformatted text preview: %change-0.5%-0.4%-0.4%-0.3%-0.3%-0.3%-0.2% Exponen±al - Exponen±al Growth to Assymptote Demand = a - br^t Upper Assymptote = a t 1 2 3 4 5 6 7 8 Demand 3.500 3.950 4.355 4.720 5.048 5.343 5.609 5.848 %change 12.9% 10.3% 8.4% 7.0% 5.8% 5.0% 4.3% Gompertz - S Curve log(demand) = a - br^t Demand = exp(a-br^t) Upper assymptote = exp(a) 2981.0 t 1 2 3 4 5 6 7 8 Demand = exp(a-br^t) 33.1 51.9 77.9 112.1 155.6 209.1 272.7 346.4 %change 56.8% 49.9% 44.0% 38.8% 34.3% 30.4% 27.0% exp(a-b)= 2981 0.0 500.0 1000.0 1500.0 2000.0 2500.0 3000.0 3500.0 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 50 100 150 200 250 300 5000 10000 15000 20000 25000 30000 35000 40000 45000 0.000 50.000 100.000 150.000 200.000 250.000 300.000 7.800 7.900 8.000 8.100 8.200 8.300 8.400 8.500 8.600...
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