William and Tingyu are studying the following problem. A reservoir contains a volume of V0 : 400 litres of pure water at time t = 0. Fort > 0, there is a constant volume inow of qm = 3 litres per minute and a larger constant volume outow of out = 9 litres per minute. The inow carries a constant salt concentration of Gin = 11 kilograms per litre. Assume the salt makes a negligible contribution to the volume and that the reservoir is well-mixed at all times. Throughout, t is measured in minutes (min), volume in litres (L), and mass in kilograms {kg}. {at} Tingyu asks you to compute the volume of salt water in the reservoir V(t) at time t g t* , where t* is the time at which the reservoir becomes empty. Vii): 25L. (b) William would like you to nd the time t* required for the reservoir to empty t\" = a if min. gynggg gggice; Enter your answer as an exact rational number. For example, write 2/3 and NOT 0 . 6666666. {6) Write down the differential equation that models the rate of change of the mass M (t) of salt in the water After expressing the equation in standard form, it will look like dM a + items) = K where the function t} is we): @minL 24 symmisg; Enter your answer as a Maple expression. For example, write 24/ (1 t) sqrt (5) for E J5 and the constant K is K: fjkg/min. In the box below, briey describe what type of differential equation this is and name the method you would use to solve it. :C [E l [is] Q II II o 9 II II :'EQEEHM s-m-Ix BIQSXaX' Styles v Font v Size v {d} William and Tingyu observe that the concentration of the outow water is given by M (t) Gout. = V(t) from which we obtain that the concentration of salt in the reservoir at time t is C(t] = 11 11 1 i1 % Explain briey why your expression for C(t) attains the expected value at t = t*. 30:: Paulette: sees: 2m 92:23:?\" $va BI exixr Styles v Font v Size ' words: 0 J