Task 9

Final Analysis!

Exponential and Logarithmic Functions

Part 1

The data in the following table shows the results of a zombie outbreak as time goes by. The number of zombies includes those that have been infected, as well as compensates for those that have been eliminated by the survivors.

Time (days)

1

2

3

4

5

6

7

8

Number of Zombies

2

4

7

11

17

35

79

150

Determine which function best models the data in the table, and then give your best approximation for what specific function would model this data, i.e. f(x) = what?

Based on the model you found, which is the best prediction of the number of zombies in 4 days (12 days since the outbreak began)?

Part 2

A hotel trying to attract new business built a banquet hall 8 years ago. The following table shows the number of events hosted in the hotel’s banquet hall each year since it was built. 

Years since built

1

2

3

4

5

6

7

8

Number of events

50

112

150

160

200

215

225

232

Is this data best represented by an exponential regression model or a logarithmic regression model? Write the equation for the appropriate regression model to the best of your abilities. 

Using your equation that you developed, predict the number of events on the 14th year.

STEP 2

Linear Programming

Mr. Walton wants to take his little brother Everett and 10 of his little friends to Chuckie Cheese. A large pizza (including tokens for games) costs $20 and a pitcher of soda costs $5.WW`

Being a teacher, Mr. Walton is very concerned about how much money he is going to spend, so he does not want to spend more than $100. Also, he is only willing to buy at most 11 pitchers of soda, but knows that he needs to have enough pizza and soda for all of the kids.

Model this scenario graphically, and then determine the best possible solutions.

STEP 3

Develop your own sequence of numbers that would sum to 100 in at most the first 25 terms, but at least the first 12 terms. It can be either an arithmetic or geometric sequence.