Question

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 70% 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:'

Answer 1

Answer:

The question has some other details missing, but here are the details ;

Write a differential equation for the time (measured in minutes) evolution of:

a) The total mass (in kilograms) of the chemical in the pond dm/dt =

b) The concentration (in kg/liter) of the chemical in the pond: dc/d t=

c) The concentration (in grams/liter) of the chemical in the pond: dc/dt =

d) The concentration (in grams/liter) of the chemical in the pond, but with time measured in hours: dc/dt =

Step-by-step explanation:

The detailed steps from first principle and the solution of each differential equation is as shown in the attached file.

starting from Concentration = mass/volume ; mass = volume x concentration, and then find the differential of both sides to generate the solved differential equation.