00:01
Hi there, so for this problem, we are given the following expression that will be one divided by the population at value t times the derivative of the population with respect to time, and then this is 0 .03, right? now in here, we can solve for the rate of change of n with respect to time, so that will be then 0 .03 times the population at any given time.
00:31
Now suppose that the population, this will be the population at a times four is equal to 100, so we need to use a linear approximation to compute the population size at a time of 4 .1, okay? so we need to find this value by using a linear approximation.
00:51
So by using a linear approximation, we will find that this at the value that we set 4 .1 will be just simply the function evaluated at four, okay? then this plus the derivative of that function evaluated at four, which is just the same as the derivative with respect to time, this is just the same, and then this times the difference between x and the value of a, where x is the value of 4 .1 and the value of a is just four.
01:27
Once we have this, then we know that this in here is 0 .1.
01:33
Now what we need to obtain is the value of the derivative of the population at four.
01:41
So what we can do is to obtain that from here because we know the population at four...