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Exponential Model: The Growth Rate Of Zombie Population

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Models Exponential Model: In exponential model, zombies increase without limitation. the function is dz/dt=k*z. k=dz/(dt*z) dz/dt is the growth rate, z is the population of zombie, and k is a constant. For k, we generated each individual k value for each data point and then took the average as the k we use, k=1.0844. z=Ce^(kt) “t” is the trial’s number and C is another constant. The C value we use is the average C value of each date point C=0.1925. So z=0.1925*e^(1.0844*t) The graph below shows the estimate values in exponential model and the actual values of zombie population for each trail. For the first five data point, the value of exponential model is close to the actual value. However, the exponential model didn’t work well for the …show more content…

The equation is dz/dx=ky(1-z/A). dz/dx is increasing rate of zombie, z is the population and A is the capacity (50). The k value we use is the average of the k values of the second to the fourth data point, k=1.0603. The function represent z in term of t is z=A-A/(B*e^kt+1). B is another constant. The B value we use is the average of each B value of each data point, B=0.0211. So z=50-50/(0.000256*e^(2.7477t)+1). The graph below shows the estimate values in logistic model and real values of zombie population. The logistic model describes both the increase of the increasing rate at the beginning and the decrease of the increasing rate at the end. However, there is still a small difference between value of logistic model and real value. To improve it, we can take zombie experiment multiple times to get more data points or enlarge the population. In conclusion, logistic model is better fit for the data than exponential model. They both describe the increasing tendency of the increase rate at first several trails. But only logistic model describes the decreasing tendency of the increase rate at the

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