00:01
Hello, so the question is population change the rabbit population on a small island is observed to be given by the function.
00:12
So given that this population can be given by the function, population function that is equal to 120 t minus 0 .4 t4 plus 1 ,000.
00:31
So where t is in time in months since observation of the island begin begin when is the maximum population attained and what is the maximum population so population will be maximum will be maximum when dp over dt is equal to zero so let us evaluate the value of d p over dt so so dp over d t is equal to differentiation of 120 t that is equal to 120.
01:20
D differentiation of t is 1.
01:22
So let me write once the formula of differentiation x to the power n is equal to n, x to the power n minus 1.
01:30
I'm using the same formula here.
01:32
Minus 4 into 0 .4, that will be 1 .6 into t q.
01:37
So this and the differentiation of thousand is 0.
01:41
So that will be equal to 0.
01:44
So from here, 1 .60 cube is equal to 120.
01:48
So from here, the value of t will be.
01:50
So let me evaluate the value of t...