Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of $\sqrt { t + 1 }$ gallons per minute, for $0 \leq t \leq 120$ minutes. At time $t = 0$, the tank contains 30 gallons of water. (a) How many gallons of water leak out of the tank from time $t = 0$ to $t = 3$ minutes? (b) How many gallons of water are in the tank at time $t = 3$ minutes? (c) Write an expression for $A ( t )$, the total number of gallons of water in the tank at time $t$. (d) At what time $t$, for $0 \leq t \leq 120$, is the amount of water in the tank a maximum? Justify your answer.
Water is pumped into an underground tank at a constant rate of 8 gallons per minute. Water leaks out of the tank at the rate of $\sqrt { t + 1 }$ gallons per minute, for $0 \leq t \leq 120$ minutes. At time $t = 0$, the tank contains 30 gallons of water.\\
(a) How many gallons of water leak out of the tank from time $t = 0$ to $t = 3$ minutes?\\
(b) How many gallons of water are in the tank at time $t = 3$ minutes?\\
(c) Write an expression for $A ( t )$, the total number of gallons of water in the tank at time $t$.\\
(d) At what time $t$, for $0 \leq t \leq 120$, is the amount of water in the tank a maximum? Justify your answer.