Can i get help answering these diff eq problems with written work please? Thanks

(1) (2) (3) (4) (5) (6) In a galaxy far, far away, on the planet Calcore, a herd of 200 Daks was introduced for breeding. Alter 4 years, the herd had increased to 600. It is determined that that rate of herd growth is directly proportional to the herd size. (a) What will be the herd size in 4 more years? (b) When will the herd size reach 16,200 Daks? The temperature of an engine at the time it is shut off is 150 C. The surrounding air temperature is a constant 30" C. After 4 minutes have elapsed, the temperature of the engine is measured at 120 C. (a) Find the temperature of the engine after another 4 minutes have passed. (b) When will the temperature of the engine reach 80625" C? (c) How long will it take for the temperature of the engine to reach 30 C? A 200 gallon tank initially contains 50 gallons of Water holding 10 pounds of salt in solution. A brine solution containing 1 pound of salt per gallon of water runs into the tank at the rate of 4 gallons per minute and the wellmixed solution runs out of the tank at the rate of 2 gallons per minute. (a) How much salt will be in the tank after 5 minutes? (b) How long will it take for there to be 55 pounds of salt in the tank? (b) How much salt will be in the tank when the tank reaches capacity? A 20 ohm resistor, a .05 farad capacitor and an alternating power force equal to 40 cos(t) are placed in series. If the initial charge on the capacitor is 3 coulombs, find the general formula for the charge on the capacitor at any time t. Chemical X is produced from a reaction involving chemicals A and B. The rate of production of X varies directly as the product of the instantaneous amounts of A and B present. The formation requires 1 pound of A for every 3 pounds of B. Assume that 20 pounds of A and 30 pounds of B are present initially and that 20 pounds of X can be formed in one hour. (a) Find the formula for the amount of X present at any time t. (b) Find the amount of X present 2 hours after the reaction begins. (c) Determine the maximum amount of X that can be formed under these conditions. The number of bacteria in a Petri dish was initially determined to be 10. Aer one hour, the number of bacteria had increased to 30 and after another hour to 60. Assume that the rate of growth of the bacteria in the dish at any time t can be calculated using the logistic equation dB = B a bB . dt ( ) (a) Determine the number of bacteria in the dish after an additional hour has passed, (b) Determine the carrying capacity of the dish based on the developed logistic equation