Putting it Together: Linear Functions

At the beginning of the module, Joan had applied for a credit card with airmiles so she could pay her regular bills with it. Her hope was to build up enough miles to take a trip. Joan has planned to use her air miles card for the following things each month:

gas = [latex]$30[/latex]
car insurance = [latex]$40[/latex]
mobile phone bill - [latex]$65[/latex]
groceries = [latex]$150[/latex]
entertainment - restaurants, movies, and live music = [latex]$50[/latex]

The total monthly expenses she plans to put on her card is [latex]$335[/latex] Each dollar she spends gives her [latex]1.25[/latex] air miles, and she expects to need about [latex]1200[/latex] air miles to buy the ticket she wants. For signing up, the card gave Joan [latex]100[/latex] free miles. Let's help Joan plan for her trip by figuring out how many months she needs to pay her bills with her card before she has enough air miles. Because she a fixed amount of air miles for each dollar spent, this is a good candidate as a linear function. Since we know the amount of air miles earned depends on the number of dollars spent, we can write a function with an input of dollars:

[latex]A(d)=\text{Number of air miles earned as a function of dollars spent}[/latex]

The initial amount of air miles Joan has is [latex]100[/latex], so our function will look like:

[latex]A(d)=100+1.25d[/latex]

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Putting it Together: Linear Functions