In this lab we use Excel to understand the differences between Linear and Exponential Functions and to reinforce our knowledge of Exponential Functions. The lab is due on Tuesday November 24, 2020 by the start of class in an Assignment Folder on ecampus. Note: You must find the functions without using the regression ability of Excel.

1. The population of Gilligans Island, located somewhere in the Pacific Ocean, has a population of 3.125 million people and is increasing at a rate of 4.1% per year. The islands annual food supply is initially adequate for 3.9 million people and is increasing at a constant rate adequate for an additional 450,000 (0.45 million) people per year. As a member of the government of Gilligans Island it is imperative that your country know if your future food supplies will be sufficient to meet the demands of your population. Use the questions below to help you prepare your document to present to the press of your country.

Directions: For this problem, you will need exactly four pages to organize and present your results. Page 1 will have parts a d, page 2 e f, page 3 g part i page 4 g part ii and h.

1. In this problem we have two different functions (one linear and one exponential), food supply and population. Describe in complete sentences the input and output variables for each function.

2. For both the food and population functions, determine, with a calculator, the output values for the input variables of 0, 1, 2, 3 and 4 and then enter these into Excel.

3. Using part b, justify which function is linear and which is exponential.

4. Find formulas for the population and food supply and write them out.

5. Enter your formulas into Excel, make a table and then graph them both on the same plot.

6. Based on your tables and graphs, approximately how many years will it be until Gilligans Island first experience shortages of food?

7. To determine the best way to extend the time before the island experiences food shortages, different scenarios are discussed below. For each one change the appropriate formula and then answer the question.

   1. Scenario 1: The rate of food production is doubled, that is it is increasing at a rate of 900,000 people per year. Make new tables and graphs for the population and food functions and use them to determine how long until the island experiences shortages.

   2. Scenario 2: The rate of the population is decreased by half, to increasing by 2.05% per year. Make new tables and graphs for the population and food functions and use them to determine how long until the island experiences shortages.

8. Based on the two different scenarios discussed in part f, which would be the best way to delay the time before there is a food shortage. Explain your answer and why it would always be the best choice.