Which scenario can be modeled by a linear function?
The area of a circle, A, can be determined using length of the diameter of the circle, d.The area of a circle, cap A comma can be determined using length of the diameter of the circle,
The number of gallons of water used, W, is based on the number of minutes, t, a fire hose is turned on if the hose uses water at a constant rate.
The number of gallons of water used, cap w comma is based on the number of minutes, t comma a fire hose is turned on if the hose uses water at a constant rate.
The number of televisions, T, a store sells each week, w, is 10, 15, 22, 17, and 18 televisions, respectively, for the first five weeks the store is open.
The number of televisions, cap t comma a store sells each week, w comma is 10, 15, 22, 17, and 18 televisions, respectively, for the first five weeks the store is open.
The population of ants in a colony, P, starts with 1,000 ants and grows by 3% every week, x.
The scenario that can be modeled by a linear function is "The number of televisions, T, a store sells each week, w, is 10, 15, 22, 17, and 18 televisions, respectively, for the first five weeks the store is open."
To determine this, we can look at the relationship between the number of televisions sold each week (T) and the number of weeks the store has been open (w). In this scenario, the number of televisions sold each week is not changing at a constant rate. That is, there is no consistent increase or decrease in the number of televisions sold as the number of weeks increases.
A linear function is characterized by a constant rate of change, meaning that the dependent variable (in this case, the number of televisions sold) changes by the same amount for each unit change in the independent variable (the number of weeks). In the scenario of the store selling televisions, there is no clear linear relationship, as the number of televisions sold each week is not changing at a consistent rate.