Hello. This covers Laplace, Linear, Bernoulli's and Linear Models. Please include clear solutions and answers. Thank you so much.

Solve the following. Write your solutions clearly and legible. Answers without solutions will not be considered. 1. The population of a town grows at the rate proportional to the population present at any time t. The initial population of 600 increases by 12% in 10 years. What will be the population in 30 years? 2. Brine containing 3 lb/gal of salt enters a tank at the rate of 4 gal/min and the solution well-stirred leaves at 4 gal/min. The tank initially contains 30 gal of water. What is the amount of salt in the tank after 5 minutes? 3. A resistance of 100 ohms and a capacitance of 0.02 farad is connected in series with a 200 volts battery. Find the charge after 0.5 second and the current after 0.4 second. dy 2y 4. + =4x3 dx X 5. xy'ty = xy+ 6. y" ty = 2t2; y(0) =1, y'(0) =0 (solve using Laplace Transform)