Reference no: EM131605641

Question: The rate at which water is flowing into a tank is r(t) gallons/minute, with t in minutes.

(a) Write an expression approximating the amount of water entering the tank during the interval from time t to time t + Δt, where Δt is small.

(b) Write a Riemann sum approximating the total amount of water entering the tank between t = 0 and t = 5. Write an exact expression for this amount.

(c) By how much has the amount of water in the tank changed between t = 0 and t = 5 if r(t) = 20e0.02t?

(d) If r(t) is as in part (c), and if the tank contains 3000 gallons initially, find a formula for Q(t), the amount of water in the tank at time t.