00:01
Hello everyone, in this question it is given that in a glass of water we add 100 g of cane sugar at t equal to 0.
00:12
So, it will change its conversion to dextrose at a rate proportional to the unconverted amount and they have given the constant of proportionality is also 2.
00:22
So, the question is we have to express this differential equation according to the rate of conversion after 10 minutes and we have to denote the amount of sugar at time t, amount of sugar at time t as q of t and further they have given q of t equal to 0 .5 is 40.
00:46
So, we have to frame the differential equation of the given statement and we have to obtain expression q as a function of t and we have to solve the differential equation.
00:57
So, let us go to the solution.
01:00
So, first we know q is equal to amount of sugar converted in t minutes then 100 minus q obviously will be is the number of grams unconverted.
01:26
So, we can write this as dq by dt is equal to k into 100 minus q.
01:33
So, since k equal to 2 we can write this as dq by 2 equal to 2 into 100 minus q.
01:40
So, the first part is over that is we have framed the differential equation for the given statement.
01:47
So, the second part is we have to just solve this equation.
01:52
So, that is differential equation.
01:54
So, we will be having.
01:56
So, this can be written as dq by dt equal to taking minus common.
02:02
So, minus 2 will be q minus 100.
02:06
So, this can be further written as dq by q minus 100 into minus 2 dt...