Which scenario can be modeled by a linear function?
A - The area of a circle A can be determined using length of the diameter of the circle D
B - the number of gallons of water used W is based on the number of minutes T a fire house is turned on if the house uses water at a constant rate
C - 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
D - The population of ants in a colony P starts with 1,000 ants and grows by 3% every week x
I think the answer is A
No, pi (D^/4) = pi R^2 is NOT linear. It is times the variable SQUARED, not proportional to the variable^1
Linear means y = m x + b
in this problem b is zero it turns out for the right answer
y = m x
typo pi (D^2 / 4)
The correct answer is B.
In option B, the scenario involves the number of gallons of water used based on the number of minutes a fire hose is turned on. This relationship can be represented by a linear function since the rate of water usage is constant (assuming the house uses water at a constant rate).
Option A does not involve a linear relationship but rather a circular relationship, so it cannot be modeled by a linear function.
Option C presents a sales pattern that does not show a consistent rate of change, so it cannot be modeled by a linear function.
Option D describes exponential growth, not a linear relationship, as the population of ants grows by 3% each week.
The correct answer is B - "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."
A linear function can be modeled by a straight line equation of the form y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept (initial value). In this scenario, the number of gallons of water used is directly proportional to the number of minutes the fire hose is turned on, assuming a constant flow rate.
To model this scenario using a linear function, you would need to collect data on the number of gallons of water used for different durations of time the fire hose is turned on. Plotting this data on a graph, if it forms a straight line, it indicates that a linear function can effectively model the relationship between the number of gallons of water used and the number of minutes the hose is turned on.