I need help with q1 and 2

3:25 pm Thu 10 Nov X orca_share_media1668043766707_9962826428752616021.pdf l. A tank holds 100 litres of pure water. A sugar solution containing 0.25 kg per litre is being run into the tank at the rate of 1 litre per minute. The liquid in the tank is continuously stirred and. at the same time. liquid from the tank is being pumped out at the rate of 1 litre per minute. After t minutes, there is in kg ofsugar dissolved in the solution. a. At what rate is the sugar being added to the solution at time t? b. At what rate is the sugar being removed from the tank at time t? e. Construct a differential equation to represent this situation. d. Solve this differential equation. c. Find the time taken for the concentration in the tank to reach 0.1kg per litre. 2. A chemical reaction is governed by the differential equation d_\\' , t - = [\\(5 .l')' d] vs here u!) is the concentration ol~ the chemical at time I. The initial concentration is zero and the concentration at time 5 s is found to be 2. Determine the reaction rate constant K and find the concentration at time It) s and 50 s. What is the ultimate value ol' the concentration? 3. Find the solutions of the following initial-value problems of the form % = f G): dt .t" .t'I: " : T~ . X( I) Z 2 (3(L)l(L QLXMS dl I (a)