Help please!
One of the earliest pollution problems brought to the attention of the Environmental Protection Agency (EPA) was the case of the Sioux Lake in eastern South Dakota. For years a small paper plant located nearby had been discharging waste containing carbon tetrachloride (CCl4) into the waters of the lake. At the time that the EPA learned of the situation, the chemical was entering at a rate of 16 cubic yards/year.

Question

anonymous · Answer

The agency ordered the instillation of filters designed to slow (and eventually stop) the flow of CCl4 from the mill. Implementation of this program took exactly three years, during which the flow of pollutant was steady at 16 cubic yards/year. Once the filters were installed, the flow declined. If t is time measured in years since the EPA learned of the situation, the rate of flow was well approximated by the following equation between the time the filters were installed and the time the flow stopped.

anonymous · Answer

Rate (in cubic yards/ per year) =$$t^{2}-14t+49$$

anonymous · Answer

(a) Graph the rate of CCl4 flow into the lake as a function of time, beginning at the time the EPA first learned of the situation. How many years elapsed between the time the EPA learned of the situation and the time the pollution flow stopped entirely?
(b) How much CCl4 entered the waters during the time shown in the graph in part (a)? Give an exact answer.

anonymous · Answer

(a) The answer is 7 years to this part.

anonymous · Answer

I am stuck on part b. Please help.

galleara · Answer

is t supposed to be time?
if so enter 7 in for t

anonymous · Answer

Yes, I entered in 7 but I got zero as an answer from the equation.

galleara · Answer

Does it give you the answer you're supposed to get? if you enter 3 for the time before you get 16.

anonymous · Answer

No, it's want a sum of all that entered over the 7 years into the water.

galleara · Answer

f=(3*16)+1/3t$$f=(3*16)+1/3t ^{3}-7t ^{2}+49t$$
$$=48+(343/3)-93$$
=69 1/3 cubic ft

anonymous · Answer

Thank you so much!
That was exactly it.

galleara · Answer

ignore the first little f= equation idk why it put that on there haha and you're welcome :)