Question

Which of the contexts below could be modeled by a linear function?
Answer
Multiple Choice Answers
Money invested in a savings account grows at an annual rate of 3%.
A car depreciates at a rate of 2.7% per year.
A taxi charges a flat fee of $4.50 for pick-up, then an additional fee of $4.50 per mile.
A radioactive compound decays at a rate of 6% per hour.

Answer 1

To determine which contexts can be modeled by a linear function, we need to identify whether the relationship between the variables is constant or changes according to a fixed rate.

1. **Money invested in a savings account grows at an annual rate of 3%**: This is exponential growth, not linear, because the amount grows on a percentage basis each year.

2. **A car depreciates at a rate of 2.7% per year**: Like the savings account, this is also an exponential decrease rather than a linear relationship.

3. **A taxi charges a flat fee of $4.50 for pick-up, then an additional fee of $4.50 per mile**: This is a linear function. The total cost (C) can be modeled as \( C = 4.50 + 4.50m \), where \( m \) is the number of miles traveled. This represents a linear increase based on the number of miles driven.

4. **A radioactive compound decays at a rate of 6% per hour**: This also describes an exponential decay, where the quantity decreases by a percentage of its current amount, not a fixed amount.

Based on this analysis, the context that could be modeled by a linear function is:

**A taxi charges a flat fee of $4.50 for pick-up, then an additional fee of $4.50 per mile.**