A tank has 300 gallons of water in it at time t = 0 hours. Water begins to be pumped into the tank at time t = 0. A different pipe is draining water from the tank starting at t = 0.
Water is being pumped into a tank at a rate modeled by the function Z(t) = 6(1.08)^t, where Z(t) is measured in gallons per hour.
Water is being removed from the tank at a rate modeled by the function P(t) = -7(0.81)^t + 12, where P(t) is measured in gallons per hour.
Is the rate at which water is being pumped into the tank increasing or decreasing at time t = 5? Justify your answer and round your calculator values to the nearest thousandth.