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(1) The half-life of Plutonium is 24,360 years. If 12g of Plutonium are released during a nuclear accident in Ohio, then how much will remain after 15,000 years? (2) A population of wolves, in a part of Alaska, numbered 200 in 1990. If there were 350 wolves in the area by 1995: Assume that the growth is obeying the Malthusian model, and predict the number of wolves in 2010. (3) A tank originally holds 10 grams of salt, mixed into 100 gallons of water. Water containing 1.5 g of salt/gallon is entering at the rate of 5 gallons/minute. If water is exiting the tank at the same rate, nd the amount of salt in the tank after time t. (4) A tank with capacity 500 gallons begins with 300 gallons of a solution, which is 2% salt. A 15% salt solution is then pumped into the tank at a rate of 4 gallons per minute. Water ows out of the tank at a rate of 3 gallons per minute. Find the amount of salt in the tank at the time when it is full (5) A cup of coffee initially at 90C cools to 75C in 4 minutes while sitting in a room at constant temperature 24C. What will be the temperature of the coffee after 10 minutes? (6) A 50-Volt electromotive force is applied to an LR-series circuit in which the inductance is 0.1 henry and the resistance is 40 ohms. Find the current m) if 1(0) = 0 . Determine the limiting CUIT 61112. (7) An 80-volt electromotive force is applied to an RC-series circuit in which the resistance is 240 ohms, and the capacitance is 103 farad. Find the charge 61(1) on the capacitor if q(0) = 0. (1) (a) Find any equilibrium points, (b) draw the slope field for the equation, (c) identify equilibrium points as stable or unstable: dv = 10 dt N (2) (a) Find any equilibrium points, (b) draw the slope field for the equation, (c) identify equilibrium points as stable or unstable: dy -= y( 4 - y) dt (3) Solve the differential equation using separation of variables. If possible state the solution as explicit for y (a) dy = 3x-y (b) dx dy x - = cos y dx dy X (c) = y (1) = 4 dx V (4) Solve using an integrating factor: dy (a) -y = ex dx (b) x dy -+y= 3x dx a+ (tan x) y = cos' x, y(0) = 2 dx (5) Show the equation is exact, and find an implicit solution: 2xty dx + x-2y dy