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 population of ants in a colony, cap p comma starts with 1 comma 000 ants and grows by 3 percent every week,
a linear function has a constant slope.
So, B
instead of all this "cap p comma" stuff, JUST WRITE P, !!
sheesh!
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 if a scenario can be modeled by a linear function, we need to check if there is a constant rate of change. In this scenario, the number of televisions sold each week is given: 10, 15, 22, 17, and 18. We can see that there is no constant rate of change because the number of televisions sold is not increasing or decreasing at a consistent rate. Therefore, this scenario cannot be modeled by a linear function.
The other scenarios mentioned are not suitable for modeling by a linear function either.
For the area of a circle, the area (A) is determined by the length of the diameter (d). Since the area of a circle is πr^2 (where r is the radius), the relationship between the area and the diameter is not linear.
For the number of gallons of water used by a fire hose, the relationship between the number of gallons (W) and the number of minutes (t) turned on is not linear because the rate of water usage can vary.
For the population of ants in a colony, the population (P) grows by 3% every week (x). Since the growth rate is not constant but based on a percentage, the relationship is not linear.
In summary, the only scenario that can be modeled by a linear function is the number of televisions sold each week because it shows a constant rate of change.