Question 29

Question 29 Samir was assigned to write an example of a linear functional relationship. He wrote this example for the assignment: The relationship between the year and the population of a county when the population increases by 10% each year. The students are allowed to use a calculator for this example. This page just shows the initial prompt. The following slides will be of Part A and Part B.

Question 29 Part A Complete the table below to create an example of the population of a certain county that is increasing by 10% a year. Year Population of a Certain County 1 2 3 4 100,000 110,000 In this part, the students are asked to come up with their own population. Each year, it will be increasing my 10%. They can choose any number, as long as it increases properly. I was thinking of doing a medium town with 100,000 people in the first year. The answers will vary but here is something to go off of. If you start with 100,000 people, then there will be that many people in the initial year of Year 0. The following year, there will be a 10% increase. That means you will need to multiply 100,000 by 10% (or .1) and add that value to 100,000. 100,000 times 10% gives you 10,000. When you add these together, you get 110,000 people in the town. For year 2, the same thing needs to happen. There will be a 10% increase on 110,000. You multiply 110,000 by 10%, and you get 11,000. You add 11,000 to 110,000 and you get : 121,000 For year 3, you multiply 10% by 121,000. That value is 12,100. You add 12,100 to 121,000 and you get: 133,100 For year 4, you multiply 10% by 133,100 and you get: 13,310. You add this to the previous value getting: 146,410 121,000 133,100 146,410

Question 29 Part B State whether Samir’s example represents a linear functional relationship. Explain your reasoning. Samir’s example is not a linear function. The population does not increase by the same amount each year, so the relationship is not linear. If something is a linear function, then it will be increasing at the same amount each time. This means that it will always increase by 10, or 20, or -500. Whatever if is, it is always the same amount. Also, if you graph it, it will be a straight line. Nonlinear functions do not increase by the same numerical amount each time. If you look at this example, you’ll see that at first, it increased by 10,000, and then 11,000, and then 12,100. Each year, it is not increasing by the same amount. Because of that, this is not an example of a linear function.