A water container is to be drained for cleansing. If Q represents the number of gallons of the water in the container t minutes after the container has started to drain, and Q(t) = 1/4 (50 − t)^2 .

Question

A water container is to be drained for cleansing. If Q represents the number of gallons of the water in the container t minutes after the container has started to drain, and Q(t) = 1/4 (50 − t)^2 .



a. Complete the following table

Q (Gallons): 625 576 529 484 - - - 324 289 256 225

t (min): 0 2 4 6 8 10 12 14 16 18 20

b. Estimate the instantaneous rate of change of Q at the instant t=8.

c. Write a sentence that clearly interprets the physical meaning of your answer in to part (b) in the context of the problem.

Answer 1

A) 441, 400, 361

B) -1/2(50-8)

=-21

=Q’(8)

C) 8 minutes after the tank started draining,

the container was instaneiously losing

21 gallons per minute.