A newly constructed fish pond contains 1000 liters of water. Unfortunately, the pond has been contaminated with 5 kg of a toxic chemical during the construction process. The pond's filtering system removes water from the pond at a rate of 200 liters/minute, removes 50% of the chemical, and returns the same volume of (the now somewhat less contaminated) water to the pond.
Write a differential equation for the time (measured in minutes) evolution of:
a) The total mass (in kilograms) of the chemical in the pond.
b) The concentration (in kg/liter) of the chemical in the pond.
c) The concentration (in grams/liter) of the chemical in the pond.
d) The concentration (in grams/liter) of the chemical in the pond, but with time measured in hours.