Generic Structures First-Order Negative Feedback

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24D-4475-2would not be conserved since the Carbon-14 is losing a beta particle (mass) to theatmosphere which is outside of the system as we modeled it).7.2 Solution to 6.2: Package Deliveries Solution1. The time constant = 2 days. The halving time ? 0.7 x time constant ? (2)(0.7) ? 1.4daysThe units for the delivery rate are packages/day.2. The goal for the system is implicitly zero.3. For 50% (1 halving time) of the packages to be delivered, Jay takes 1.4 days. For 75%(2 halving times) of the packages to be delivered, Jay takes 2.8 days.7.3 Solution to 6.3: Company Downsizing1. The time constant = 2 years, which is the adjustment time. The draining fraction =1/time constant = 0.5.The halving time ? 0.7 x time constant = (0.7)(2) = 1.4 years.2. In 3 years about 2 halving times go by. In two halving times, about 75% of the initialgap is filled. 75% of 8000 is 6000, therefore (20,000 - 6,000 ) 14,000 employees are stillworking at Nanosoft.3. In 4 years, Nanosoft wants 4,000 workers fired. This is 50% of the gap and shouldtake 1 halving time. If 1 halving time = 4 years, the adjustment time ? halving time/ 0.7? 4/0.7 = 5.7 years. Nanosoft should increase the adjustment time to 5.7 years.8 AppendixModel Documentation for Sections 2.1 to 2.3Section 2.1: Radioactive Decay Model Documentationradioactive compound(t) = radioactive compound(t – dt) + (– rate of decay) * dtINIT radioactive compound = a constantDOCUMENT: This is the amount of radioactive compound present.
D-4475-2 25UNIT: atomsOUTFLOWS:rate of decay = radioactive compound * decay fractionDOCUMENT: This is the amount of radioactive compound that turns into a stablecompound per year.UNIT: atoms/yeardecay fraction = a constantDOCUMENT: This is the draining fraction of the negative feedback system.UNIT: 1/timeSection 2.2: Population-Death System Model Documentationmule population(t) = mule population(t – dt) + (– death rate) * dtINIT mule_population = a constantDOCUMENT: This is the number of live mules in the systemUNIT: mulesOUTFLOWS:death rate = mule population * death fractionDOCUMENT: This is the number of mules that die per year.UNIT: mule/yeardeath fraction = a constantDOCUMENT: This is the draining fraction of the negative feedback system.UNIT: 1/years
Page 1 and 2: D-4475-2 1Generic Structures:First-
Page 3 and 4: D-4475-2 3Table of Contents1. INTRO
Page 5 and 6: D-4475-2 5
Page 7 and 8: D-4475-2 71. IntroductionGeneric st
Page 9 and 10: D-4475-2 9A simple negative feedbac
Page 11 and 12: D-4475-2 11number of employeesfirin
Page 13 and 14: D-4475-2 13flow = adjustment gap *
Page 15 and 16: D-4475-2 153.3 Model BehaviorThe ch
Page 17 and 18: D-4475-2 171: STOCK 2: STOCK 3: STO
Page 19 and 20: D-4475-2 195. Summary of important
Page 21 and 22: D-4475-2 21To sum up, asymptotic gr
Page 23: D-4475-2 23Figure 12. Company Downs
Page 27 and 28: D-4475-2 27Vensim Examples:Generic
Page 29 and 30: D-4475-2 292.2 Example 2: Populatio
Page 31 and 32: D-4475-2 31The initial time for the
Page 33 and 34: D-4475-2 33(05) GOAL FOR STOCK=a co
Page 35 and 36: D-4475-2 35Graph of Stock with diff

Generic Structures First-Order Negative Feedback

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