Week	New Cases	Cumulative Cases
1	49	49
2	191	240
3	369	609
4	331	940
5	333	1273
6	571	1844
7	742	2586
8	955	3541
9	1029	4570

10	883	5453
11	682	6135
12	512	6647
13	412	7059
14	381	7440
15	343	7783
16	256	8039
17	247	8286
18	142	8428
19	82	8510

20

71

8581

1. There is yet another type of model of growth we can consider for this data set: logistic growth. A logistic growth function has a maximum "population" called the carrying capacity. As the "population" grows over time, the number of things in the "population" grows to the carrying capacity and stays there. This capacity represents the maximum amount the environment can sustain. So back to our data...The population of French Polynesia at the time of the outbreak was about 270,000. Performing logistic regression on the data set for weeks 1 to 20 gives the following growth equation:

y= 8480.68 / 1+45.7918e^-0.432235t

1. Graph this logistic growth model with the data set for weeks 1 through 20 and give the graph below(this should include 1 to 20 on the horizontal, the data points, and the logistic graph together, appropriately labeled).

1. Discuss whether the logistic growth model would be a good fit for the given data using a few sentences in context of the problem.
3. Is there a number of weeks after which this model would be irrelevant or not useful for this specific scenario? Explain fully.
4. Use this logistic growth model to predict the number of cumulative cases after 40 weeks. Give your answer rounded to two decimal places.
5. Discuss this model in comparison with the others given in this project, and how it may or may not be better for prediction in this situation.