Final answer:
The contexts that can be modeled by a linear function are those with a constant rate of change. Susan's weekly savings, Ariel and Miguel's daily car rental cost, and Monica's annual car insurance payment plus a constant increase can all be modeled as linear functions, making option c) 3 and 5 the correct answer.
Step-by-step explanation:
The contexts that could be modeled by a linear function are scenarios where the relationship between the two variables is constant; this means that the change in the dependent variable is the same for any equal change in the independent variable. Reviewing the given scenarios:
- The value of David’s car decreases by 11% each year. (Not Linear)
- The amount of Ariel and Miguel rent a car for $40 a day.
- The price of a stock each week is 105% of its price from the previous week. (Not Linear)
- Monica pays $700 for car insurance the first year and pays an additional $10 per year.
The first scenario is linear because it represents a fixed amount being added each week, which would be a constant slope on a graph. The third scenario is also linear because the cost per day is constant, indicating a fixed rate of change. The fifth scenario exemplifies a constant initial amount with a constant yearly addition, which is linear as well. However, the second scenario involves a percentage decrease, which represents exponential decay, not linear change. The fourth scenario also involves a percentage change, indicating exponential growth, not a linear relationship. Therefore, the linear contexts are the first, third, and fifth scenarios.
The correct answer to the question is therefore c) 3 and 5.