Question

The rate at which raw sewage enters a tank is E(t). for 0 <= t <= 4, the cost of treating the sewage at time t is .15-.02t
the answer sheet says the answer is the integral from 0 to 4 of (.15-.02t)E(t) dt, but i wonder: why do you multiply them?

Answer 1

i do not know how they came up with that answer

Answer 2

they want the total cost right?

Answer 3

yes

Answer 4

\[\int\limits_{0}^{4} (.15-.02t)*E(t)dt = total cost\]