Big Ideas Math Algebra 2 A Bridge to Success
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Big Ideas Math Algebra 2 A Bridge to Success View details
3. Modeling with Linear Functions
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Exercise 3 Page 21

In general, to use a linear function to model and analyze a real-life situation, you need to start by defining the variables.

See solution.

Practice makes perfect

We are asked how we can use a linear function to model and analyze a real-life situation.

Theory

Before writing the function to model and analyze the situation, we first need to define the variables. Then, we will write the equation that connects them. Finally, we use the model to find the desired values. Let's see a real-life situation.

Real Life Situation

Paula is spending her holidays in Portugal, and wants to rent a bike for a few days. She saw an advertisement at a local shop. Calculate the price of renting a bike for one week. How many days can she rent a bike if she plans on spending

Rent a bike!
per day plus a one-time payment of

Let's use a linear function to model the above situation. Let be the number of days Paula rents the bike, and the cost of renting the bike for days.

Verbal Phrase Algebraic Phrase
,
We have found the linear function to model the situation.
To find the cost of renting a bike for days, we substitute for in the above formula, and solve for
The cost of renting a bike for a week is To find the number of days that a bike can be rented for we substitute for and solve for the variable.
Solve for
With Paula can rent a bike for days.