00:01
In this problem, we are given a dorm at a college houses as 11 ,000 sorry 1 ,100 students.
00:16
One day, 20 of the students became ill with flu.
00:31
So, we are given the total number of students who are being instructed.
00:38
So, total is given in the term of general.
00:41
So, n of t is equals to 1 ,100 over 1 plus 16 e raised to the power of negative 0 .65 t.
00:52
So, in the first subdivision, we have to find after how many days is the flu spreading faster.
00:59
So, first let us say this as equation 1.
01:04
So, first let's differentiate this.
01:06
So, n dash of t is equals to 1 ,100 multiplied by 16 multiplied by negative of 0 .65 raised to the power of e raised to the power of 0 .65 t over 1 plus 16 e raised to the power of negative 0 .65 t the whole square.
01:33
This is the differentiation of n of t.
01:36
So, let's write this in the format of n dash of t is equals to 0 .65 n of t multiplied by 1 subtracted by n of t over 1 ,100.
01:54
So, i am going to keep this as equation 2.
01:57
So, now again, we have to differentiate this term with respect to t to find the maximum of the given terms.
02:07
So, we have to again equate n dash of t is equals to 0.
02:11
So, for that, let's find n double dash of t.
02:17
So, n double dash of t is equals to 0 .65 n of t 1 negative of n of t over 100 multiplied by n dash of t.
02:29
So, this is what n double dash of t looks like.
02:34
So, from this equating equate this term with 0, we will be getting 0 .65 n of t multiplied by 1 subtracted by n of t over 100 multiplied by n dash of t is equals to 0.
02:51
So, from this we get n is equals to 500 sorry 550 which implies 1000 over 1 plus 15 sorry 16 e raised to the power of negative 0 .65 t is equals to 550.
03:23
So, solving this will give us t.
03:29
So, let's solve.
03:30
So, we have 550 multiplied by 1 plus 16 e raised to the power of negative 0 .65 t is to 1100...