Final answer:
The equation that relates the number of gallons to the time is g = 2.2t, which represents a linear function because the rate of change is constant, indicating a straight line graph.
Step-by-step explanation:
To write an equation that relates the number of gallons, g, to the time, t, we can use the information given. At t=5 minutes, there are 11 gallons of water, and at t=10 minutes, there are 22 gallons of water. We can see that the amount of water in the tub increases at a constant rate, as the number of gallons doubles from 5 to 10 minutes. This suggests a linear function.
Since the rate is constant, we can find the slope of the line, which is (22 gallons - 11 gallons) / (10 minutes - 5 minutes) = 11 gallons / 5 minutes = 2.2 gallons/minute. The function starts at t=0, so there is no initial value other than zero for the gallons. Therefore, the equation that represents this relationship is g = 2.2t.
Yes, the relationship represents a linear function because the rate of change is constant, which means that for each additional minute, the same amount of water (2.2 gallons) is added to the tub. Hence, the graph of this function would be a straight line, which is a characteristic of linear functions.