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.
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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.
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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.
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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.
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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.
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