00:01
In this question, we are considering decomposition or growth for first order differential equation.
00:11
Now, here let initial dissolved oxygen, initial dissolved oxygen in water, oxygen in water is denoted by l0.
00:27
At time t equals to 0 initially.
00:31
Now, rate of decomposition of dissolved oxygen is directly proportional to the do that is the dissolved oxygen present at any time that is represented by l.
00:54
So, so, this implies rate of change of l with respect to time is directly proportional to minus l.
01:03
Negative sign shows that it is decreasing with the time.
01:07
Now, to remove this directly proportionality, we will write this dl upon dt equals to kl minus kl where k is the proportionality constant.
01:20
Now, this can be written as dl upon l equals to.
01:25
Minus k dt.
01:27
Now integrating both side with respect to t...