00:01
So for this problem, we're told that a population of insects follows the exponential growth model.
00:08
At first, so the population at the time equals to zero is given, and that is equal to 5 ,000 insets.
00:19
And two days later, there are 2 ,000 insects.
00:24
So as you can see, the population has decreased.
00:28
So after two days.
00:33
So the population at the time of two days is 2 ,000 insects.
00:41
So the question is how many insets are present after six days from the star? so we want the population after six days.
00:51
Now, we want a well, we are told for this problem that the population follows the exponential growth model.
00:58
And the population growth model has that the population is equal to the initial population, p -sub -0, which corresponds to the value that we are given for initially, this times the exponential of a constant of proportionality k that we need to determine, and this times the time.
01:20
So the first thing that we need to do is to determine the constant of proportionality k by using the conditions that we are given.
01:27
So let's first write the equation as it should be.
01:31
So we will have that initial population p .0 corresponds to the population at the time equals to zero.
01:37
That is 5 ,000 times the exponential of k times the time.
01:44
Now, to determine the value of the concept of proportionality k, we can use the second condition that we are given, that the population after two days is two, thousand insets.
02:02
So we applied that in here, so we will have 2 ,000 is equal to 5 ,000 times the exponential, the constant, and this times the time that has passed, that is two days...