Water is being pumped into a tank at a rate of R(t) = 82t gallons per minute over the interval 0 t 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons.

a) How many gallons of water are pumped into the tank during the entire 8-minute interval?

b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer.

c) Determine the amount of water in the tank at time t = 2.

d) Assume water continues to be pumped into the tank and leaks from the tank at the given rates after t = 8 minutes. Write, but do not solve, an equation that gives the time k at which the tank reaches its capacity.

No calculator is allowed for the following problem. Water is pumped into a tank at a rate of R(t) = 8J2? gallons per minute over the interval 0 s t s 8. Water leaks out of the tank at a constant rate of 2 gallons per minute. The tank originally contains 10 gallons of water and can hold 200 gallons. a) How many gallons of water are pumped into the tank during the entire 8-minute interval? b) Is the amount of water in the tank increasing or decreasing at time t = 2? Justify your answer. c) Determine the amount of water in the tank at time t= 2. d) Assume water continues to be pumped into the tank and leaks from the tank at the given rates after t = 8 minutes. Write, but do not solve, an equation that gives the time k at which the tank reaches its capacity