Question

A tank is being filled with water at a constant rate of 800 gallons per minute. The initial amount of water contained in the tank is 120 gallons.

a) Write down a linear function that represent the total number of gallons V in the tank after t minutes.
b) What does 800 represent? The average decrease/increase in y ____________ for each x _____,
c) How do you represent this function?
d)Y _________________ as a function of x _______________________.

Answer 1

A linear function representing the water volume in the tank is V(t) = 800t + 120. The 800 represents the rate of water flow into the tank in gallons per minute. The function can be graphically represented as a straight line with time on the x-axis and volume on the y-axis.

Step-by-step explanation:

To answer the student's question:

(a) A linear function that represents the total number of gallons V in the tank after t minutes can be written as V(t) = 800t + 120. This equation takes into account the initial amount of water and the constant rate at which the tank is being filled.

(b) The number 800 represents the average increase in V (gallons) for each increase in t (minutes).

(c) This function can be represented graphically as a straight line on a graph where the horizontal axis (x-axis) is the time in minutes, and the vertical axis (y-axis) is the volume of water in the tank in gallons.

(d) V increases as a function of t where t is the number of minutes since the tank started being filled.