In the real world, it is more common to have data that is approximately linear than exactly linear. These activities will introduce the idea of linear trends, which we’ll spend more time on in class. They’ll also provide practice with building a linear model by identifying its slope and vertical intercept.
Several years ago, Onondaga Community College, in upstate New York, introduced a meal plan that included “Flex Dollars” that were stored on students’ ID cards. Each student was given $150 “Flex Dollars” as part of their meal plan package that could be used like cash at several campus dining locations.
Let \(M(t)\) be the amount of money left on the card, \(t\) weeks after the beginning of the semester. Write a linear equation to model the data. Use Week 0 and Week 14 to calculate the slope.
If Loralee continues to spend her flex dollars at the same rate, use your equation to determine how much money will be on the card at the end of spring semester, which also lasts 14 weeks.
Smartphones, like many other manufactured goods, depreciate on a daily basis. Depreciation means how much an item (e.g. a smartphone) loses in value compared to the price that was originally paid for it from the manufacturer. There tends to be two main periods in a smartphone’s life when it sees the biggest drops in value: 1. the period of time after the phone is initially purchased, and 2. when the manufacturer launches a new model.
In September 2019, the iPhone 11 256GB was released with a price of $849. Twelve months after the launch, it was found that the value of iPhone 11s depreciated about 37% (which is actually better than most smartphone depreciation!). 1
Suppose Coraline bought a new iPhone 11 256GB in September 2019 for $849. The phone would soon start depreciating in value. The following table shows the approximate value of her iPhone 11, by month from September 2019.
It can be easier to work with models when the data are numerical. Modify the first row of the table to change the months into numbers. There isn’t a “right” way to do this, although it is important that Jan 2020’s number be bigger than Dec 2019’s.
Write an equation that gives a linear model for the value of the cell phone from Sept 2019 through February 2020. Use \(V(m)\) for the value in dollars, \(m\) for the number of the month, and your slope estimate.
Suppose Coraline wants to sell her phone before it is worth less than $300. Using your model, when is the last month she could sell it and get at least $300?
You’ll need to be able to do the following things for this lesson. Rate how confident you are on a scale of 1 - 5 (1 = not confident and 5 = very confident).
