Final answer:
In the equation w = at + b, the value of 'a' is 8 because the tank is filled at a rate of 8 gallons per minute, and the value of 'b' is 50 because the initial volume of water in the tank is 50 gallons.
Step-by-step explanation:
The values of a and b in the linear equation w = at + b, which represents the total amount of water w in gallons that the water tank will have after t minutes, can be determined based on the initial condition and the rate at which the tank is being filled.
The value of b represents the initial amount of water in the tank before it begins to be filled, which is given as 50 gallons. Therefore, b = 50.
The value of a represents the rate at which the water is being added to the tank, which is 8 gallons per minute. Hence, a = 8.
Putting these values into the equation, we get w = 8t + 50.