the electric charge, in coulombs, on a spherical surface leaks off at a rate proportional to the instantaneous charge. initially, 5 coulombs are present, and one-third leaks off in 20 . whe l there be 1 coulomb remaining? 4. a1 liter tank is filled with a salt solution containing 4 grams of dissolved salt. at t = 0, a hole is drilled in the bottom of the tank and the solution drains out at 을 liters per minute. at the same time, fresh water is being pumped in at , liters per minute. let a(t) be the amount of salt in grams after t minutes a) find a formula for r(t) by solving the appropriate differential equation b) how long will it take until 1 gram of salt is left in the tank? 5. carbon dating is often used to determine the age of a fossil. for example, a humanoid skull was found in a cave in south africa along with the remains of a campfire if m(t) is the mass of carbon-14 in the fossil after t years, then the rate of change of mass with respect to time is proportional to the mass: dm dt -am (where λ is a positive constant) solve the differential equation and obtain a formula for m(t). show all steps. it is detrmined that only 2% of the original amount of carbon-14 remains in the burnt wood of the campfire. estimate the age of the skull if the half-life of carbon-14 is 5600 ears