00:03
In this problem, we're told that a strain of bacteria grows at a rate proportional to the square of the size of the population.
00:16
So again, let's make the population of the bacteria be y equal to f of t at time t.
00:41
So at the size of the initial population, we know that y of zero cannot be equal to zero.
00:51
So the solution would become a zero solution, which is invalid to the current problem.
01:08
So we have to have a differential equation that states that dy over dt is directly proportional to y squared.
01:26
So that states that dydt, dy over dt, is equal to k, a constant, of proportionality times y squared.
01:48
And again, we know the initial condition, y of zero is not equal to zero, and that k is greater than zero.
02:07
So again, you could just graph that...