00:01
Hello students, let us consider x be the number of students who are infected by flu virus.
00:25
Here the total number of students is 1000.
00:39
Therefore, the total number of students who are not affected is 1000 minus x.
01:03
Let us consider the rate at which the virus is spreading that is dx by dt equal to kx into 1000 minus x.
01:16
By separating the variables, we will get 1 by 1000 into 1 by 1000 minus x plus 1 by x into dx equal to k into dt.
01:33
Here we have to integrate on both sides.
01:35
Therefore, 1 by 1000 integral 1 by 1000 minus x plus 1 by x into dx equal to k into integral dt.
01:55
By integrating this, we will get 1 by 1000 into minus log 1000 minus x plus log x equal to k into t plus c.
02:15
Here it can be written as log of x by 1000 minus x equal to 1000 into kt plus c.
02:31
Therefore, we can rewrite this as x by 1000 minus x equal to e power 1000 kt plus c where c is the integration constant.
02:43
Therefore, it can be written as x by 1000 minus x equal to c e power 1000 kt.
03:04
Initially, one student carry a flu virus to an isolated college campus such that it can be written as t equal to 0 where x of 0 equal to 1.
03:16
Therefore, by applying this in the above equation, we will get 1 by 999 equal to c...