Jack and Diane live in a small town of 50 people. Unfortunately, both Jack and Diane have a cold.Those who come in contact with someone who has this cold will themselves catch the cold. The following data represent the number of people in the small town who have caught the cold after t days.

Days, t ……………………… Number of People with Cold, C0

0 ………………………………………………………..…. 2

1 ……………………………………………………….…. 4

2 ……………………………………………………….…. 8

3 …………………………………………………………. 14

4 …………………………………………………………. 22

5 …………………………………………………………. 30

6 …………………………………………………………. 37

7 …………………………………………………………. 42

8 …………………………………………………………. 44

(a) Using a graphing utility, draw a scatter diagram of the data. Comment on the type of relation that appears to exist between the days and number of people with a cold.

(b) Using a graphing utility, build a logistic model from the data.

(c) Graph the function found in part (b) on the scatter diagram.

(d) According to the function found in part (b), what is the maximum number of people who will catch the cold? In reality, what is the maximum number of people who could catch the cold?

(e) Sometime between the second and third day, 10 people in the town had a cold. According to the model found in part (b), when did 10 people have a cold?

(f) How long will it take for 46 people to catch the cold?