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Instructions: Solve each problem using any type of mathematical software, preferably matlab, show the result of each question with a screenshot of what the software shows and a graph. Solve it as differential equations. 1. When taking a cake out of the oven it has a temperature of 300F. If the temperature of the cake in a time function is the following dT dl - 3 1 In T(I) - 300 a) After 3 minutes in the oven, we take the cake out, the temperature is 200F, how much time will it take for temperature of the cake to get to 80 F. b) Make a graph with the cake's temperature in a time function for 051525 minutes. 2. After holding a mass of 10 pounds of weight in a spring of 5 feet, the spring is now 7 feet. This massis changed for a new one that weighs 8 pounds. All the system is now placed in a way of absorption that is the same as the instantaneous velocity. a) Graph the equation of movement if the mass is released from a point that is 12 inches under the equilibrium position, the velocity goes up to 1 ft/s, for 051<35 seconds. b) At what moment the mass crosses the equilibrium position. (the first two times that this happens) 1 5x = 0; x(0) = 0.5; x'(0) = 4 3. Assume that a tank has initially 100 gallons of water in which they dissolve 50 pounds of salt. Another salty solution is pumped inside the tank with a velocity of 3 gallons per minute. If the concentration of the solution that is going inside the tank is 2lb/gal. Show the amount of pounds of salt in the tank in 20 minutes and make a graph of the amount of salt in the tank in a time function for USIS70 minutes. X(t) show the amount of salt present in the tank in time t. dx 1 x - 6, x(0) = 50 100 4. Determine the general solution for the differential equation system and make a graph of each solution in at function: dr 4x dt 2y di + 2 xx(0) = 1; y(0) = 2

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