Which situation could be modeled by a linear function?
A. A bank account that grows at a rate of 5% per year, compounded annually
B. A population of bacteria that doubles every 4.5 hours
C. The cost of cell phone service that charges a base amount plus 20 cents per minute
D. The concentration of medicine in a person's body that decays by a factor of one-third every hour
C. The cost of cell phone service that charges a base amount plus 20 cents per minute
The situation that could be modeled by a linear function is option C - the cost of cell phone service that charges a base amount plus 20 cents per minute.
A linear function is a mathematical model that represents a relationship between two variables in a straight line. In this case, we need to identify a situation that can be represented by a linear function.
A. A bank account that grows at a rate of 5% per year, compounded annually:
This situation does not represent a linear function because the growth rate is compounded annually, meaning it would not be a straight line.
B. A population of bacteria that doubles every 4.5 hours:
This situation does not represent a linear function. The population doubling every 4.5 hours indicates exponential growth, not a linear relationship.
C. The cost of cell phone service that charges a base amount plus 20 cents per minute:
This situation can be represented by a linear function. We can define the cost of cell phone service as a function of the number of minutes used. The base amount represents the fixed cost, and the additional charge per minute defines the rate of change. We can express this situation using a linear equation.
D. The concentration of medicine in a person's body that decays by a factor of one-third every hour:
This situation does not represent a linear function. The decay of the medicine by a factor of one-third indicates an exponential decay, not a linear relationship.
So the situation that could be modeled by a linear function is C, the cost of cell phone service that charges a base amount plus 20 cents per minute.