A linear function represents a relationship where the change in one variable results in a constant change in another variable. In other words, it describes a situation where the rate of change is constant.
Let's evaluate each option:
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A bank account that grows at a rate of 5% per year compounded annually: This situation represents exponential growth, not linear growth, because the interest earned each year increases as the account balance increases. Not linear.
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A population of bacteria that doubles every 4.5 hours: This situation is also exponential growth, as the population increases by a factor of 2 at regular intervals. Not linear.
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The cost of a cell phone service that charges a base amount plus 20 cents per minute: This scenario can be represented as a linear function because the cost increases by a constant rate (20 cents) for each additional minute of service, plus a constant base amount. This is in the form \( C = b + 0.20m \), where \( C \) is the total cost, \( b \) is the base amount, and \( m \) is the number of minutes. Linear.
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The concentration of medicine in a person’s body that decays by a factor of one third every hour: This situation describes exponential decay, as the concentration decreases by a fraction of its value rather than by a fixed amount. Not linear.
In summary, the only option that could be represented by a linear function is:
The cost of a cell phone service that charges a base amount plus 20 cents per minute.
1 answer