Question

A newly constructed fish pond contains 3000 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:

Answer 1

Answer:

$\frac{dm}{dt}=-\frac{m}{30}$

Step-by-step explanation:

We are given that

Volume of water in fish pond,V=3000 L

Mass of toxic  chemical=5 kg

Rate=200L/min

Removes chemical=50%

We have to find the differential equation for the time.

Let mass of toxic at any time t= m kg

Rate=Rate in-Rate out

$\frac{dm}{dt}=200\times 0-\frac{m}{3000}\times 200\times \frac{50}{100}$

$\frac{dm}{dt}=0-\frac{m}{30}$

$\frac{dm}{dt}=-\frac{m}{30}$