# Growth and decay

A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets

contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank.

Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters the tank at a rate of 'R' liters per minute, and the completely mixed solution leaves at the same rate.

a) If 'P0' is the amount of pollutants in the tank at time t=0 then find 'P(t)' for any time t.

b) If k=0, find the time 'T' for the waste to be reduced to 40% of its original value.

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#### Solution Preview

The key idea in this problem is to identify the time-dependent variable and to formulate the differential equation that governs it. The differential equation will give the behavior in time of the variable quantity which will help us evaluate the various quantities the problem asks.

Note: This problem does not use numerical quantities but deals with the equations.

In our case, the time-dependent variable is the concentration of pollutants i.e. ...

#### Solution Summary

This shows how to find the amount of pollutants in a tank and the time for the waste to be reduced to a given value for a specific crude-oil refinery situation.