An object is taken from an oven at 425 F and left to cool in a room at 70"F. After - hour, the temperature fell to 3250F. (a) Find a formula for the temperature of the object at any time t. (b) What will be the temperature of the object after 2 hours? - . . (a) T(t) = (Type an exact answer in simplified form. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.)holds a 138 gal solution of water and salt. Initially, the solution contains 19 lb of salt. A salt solution with a concentration of 2 lb of salt per gal begins flowing into the tank at the rate of 3 gal per minute. The solution in the tank also begins flowing out at a rate of 3 gal per minute. a. Find an expression for the amount of salt in the tank at any time. b. How much salt is present after 45 minutes? a. The amount of salt in pounds, y, in the tank after t minutes is given by the following equation. y =]For the following stirred tank reaction, carry out the following analysis. a. Write an initial value problem for the mass of the substance. b. Solve the initial value problem and graph the solution to be sure that m(0) and lim m(t) are correct. 1-700 A one-million-liter pond is contaminated and has a concentration of 70 g / L of a chemical pollutant. The source of the pollutant is removed and pure water is allowed to flow into the pond at a rate of 1100 L/ hr. Assuming that the pond is thoroughly mixed and drained at a rate of 1100 L/ hr, how long does it take to reduce the concentration to 50% of the initial value? O A. m(t) = 70,000,000 - e - U.00171 B. m(t) = 70,000,000 e - 0.0011t O C. m(t) = e -0.0011t - 70,000,000 O D. m(t) = - 70,000,000 e - 0.00111 Graph the solution to be sure that m(0) and lim m(t) are correct. Choose the correct graph below. Each graph is shown in a [ - 1000,6000,500] by [0,75000000,5000000] viewing window. 1-+ 00 O B. O c. O D. TTTTTT It will take about hours to reduce the concentration to 50% of the initial value.A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Supposed that the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time t= 0, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 400 -. The inflow rate is 0.04 -. Assume that the drug is quickly mixed thoroughly in the blood and that the volume of blood remains min constant. Complete parts a through d below. O B. O C. OD. Choose the correct graph below of the concentration of the drug. Each graph is shown in a [0,500, 100] by [0,400,100] viewing window. O A. B. O C. OD. c. What is the steady-state mass of the drug in the blood? The steady-state mass of the drug in the blood is mg