00:01
Hi, in this question first we need to formulate the equation of the mass.
00:06
Here, given that a substance is transformed at a rate proportional to a mass of the substance at that time.
00:15
So, dm divided by dt directly proportional to m.
00:19
On changing the directly proportional to equal so we have to add the constant.
00:24
So, dm divided by dt equals km.
00:28
It can be rewrite as dm divided by m equals k into dt.
00:34
On integrating both sides then we get log m equals kt plus c.
00:42
Here, given that original mass is 50 grams so m equals 50 gram at t equals 0.
00:52
On substituting in this then we get log 50 equals 0 plus c.
00:58
So, c equals log 50.
01:01
On substituting in this then we get log m equals kt plus log 50.
01:12
And here, given that t equals 200 then m is decreased by 20 gram.
01:21
So, initial as 50 minus 20 which is equal to 30 gram...