# Systemic Thinking

Understanding Delays. 2.2 Studying the First Order Negative Feedback System with Excel I program the system in Excel and carry out further experiments.

I also notice the programming task becomes much easier. 2.2.1 First Order Negative Feedback Loop Responseto a Step in the The first driver function I use for the First Order Negative Feedback model is the Step. First Order Negative Feedback System Structure I formulate the model in the spreadsheet as per the below. System Response to Step in the Inflow Rate Note: the Level increases until the outflow rate rises to equal the inflow rate.

This test confirms my sketch. 2.2.2 First Order Negative Feedback Loop Responseto a Step in the Target I continue to experiment with the Step function. Target as Driver System Response to Step in the Target Note: the Level increases by the value of the Target i.e. 5 cups. The Gap decreases from a value of 8 cups to 3 cups at time = 2 seconds and then grows asymptotically by 5 cups to its initial value of 8 cups. Inflow Rate as Driver. 4.5 - Exponential and Logarithmic Models. Exponential Growth Function y = C ekt, k > 0 Features Asymptotic to y = 0 to left Passes through (0,C) C is the initial value Increases without bound to right Notes Some of the things that exponential growth is used to model include population growth, bacterial growth, and compound interest.