It is clearly true that nothing could exponentially grow forever, after all, it would be impossible for the number of people with some disease that shall not be named to exceed the world's population. Now, you might be thinking: "Scientists and mathematicians are stupid. Their models don't work." Well, if you thought that you are wrong. The reason you are wrong is because scientists and mathematicians would actually model this situation with a logistic model. Let us suppose we are trying to model the population of rabbits in some park. Let us further suppose that 950 we model the population of rabbits as: N = where, t is measured in years. This would be an 1 + 9e -0.5t example of a logistic model. In this problem we are going to investigate some properties of logistic models. 950 IfN 1 + 9e - 0.5 gives the population of rabbits in a park as a function of t as measured in years, answer the following questions: a) Using a calculator, produce a plot of N. Adjust the plot window so as to see the behavior of the function. In your work page, sketch the plot and upload a scan. Choose File No file chosen b) Find the initial population of rabbits in the park. c) Find the time it takes for the population of rabbits to double from its initial value (round your answer to the nearest tenth of a year.) d) Logistic models are characterized by a carrying capacity. Based on your plot, what is the carrying capacity of rabbits in this park