Question

This is 2 questions to a tutorial on how to stop a zombie apocalypse by coming up with functions that model the spread of zombies and finding key points in time using your function. (If we get through this entire section: I will write a very long letter of gratitude and give you the highest rating for helping me understand. I truly just want to finish) There are only steps, so this should be easy, but I need help! (Total of questions: 2) Please include some work and a bit of an explanation, so I know how to approach more problems like this. ( Some of these numbers are rather large, so I’ve been using the web2.0 calculator to hold the numbers- making it easy on myself ) Step 1: create a function using the information from the report and the interviews to create a function that models the growth of the zombie population. In order to get a function that models the spread of zombies, you obtain this information: -locals inform you that they seen them stumbling in tattered clothes and causing a disturbance at a local cemetery , where the zombies were found has 100 plots, which are all filled. -Doctor states that his studies indicate that these zombies can spread at a rate of 20% -We know that the population of the U.S is 325,000,000. Therefore, the population of zombies in the country CANNOT exceed that number. (With all of the information collected, use the data to set up a function that represents the spread of the population of zombies. the total number of zombies is limited by the total number of humans that exist. Here are the types of functions that you need to know about the mathematical model and it’s description: Exponential growth- determines the amount of uninhibited growth over a period of time Gaussian functions- used to model data that assumes a normal bell-snapped curve. Logistic Growth- determines the amount of growth over time when there is a limit to the total population. (There is a limit to the population that the zombies can reach, so the growth much be modeled by logistic growth. ) •L (x) = a/1+ be^rx•Let a represent the capacity of the population, must be positive •Let r represent a positive real number for the growth rate •Let x be the independent variable representing the elapsed time •B is a real number constantIN your function the independent variable •x, will be in the number of daysHERE IS WHAT I HAVE SO FAR : A=350,000,000R in decimal form = 0.2NOW that that’s out of the way, HERE IS WHAT I NEED MOVING FORWARD: 1. Assuming that all of the people buried in the cemetery were reanimated, what does L(x) equal at the very start of the zombie apocalypse (at x=0 days)? NOW that you have identified the capacity, rate of growth, and initial population, use this information to find the constant, b, and complete the logistic grown function that models the spread of the zombie population. 1. What is your logistic growth function for the growth of the zombie population? Please include work so I can see how I’m supposed to go about completing more like this.

Answer 1

The first thing we have to know is that logistical growth is the per capita growth rate of a population that gets smaller and smaller as the size of the population approaches a maximum number of people. In the case of the zombie apocalypse, the dead would not count and the maximum population number would be the population of the U.S is 325,000,000.

`\begin{gathered} L(x)=(a)/(1+be^(-rx)) \\ a=325,000,000\to\text{USA population} \\ r=0.2\to\text{growth rate} \\ x\to\text{time in days } \\ b\to\text{constant} \\ \approx \end{gathered}`

For x = 0, they found 100 open graves so with this information we can find b

`\begin{gathered} 100=(325,000,000)/(1+be^(-0.2(0))) \\ 1+b=(325,000,000)/(100) \\ b=3,250,000-1 \\ b=3,249,999 \end{gathered}`

Then the growth equation will remain

`L(x)=(325,000,000)/(1+3,249,999e^(-0.2x))`