00:02
Problem 12 of section 7 .1 asks for the equation of a given bacteria culture.
00:09
So the first thing that we need to do to solve this problem is we need to write out the general solution to differential equations, which, as we know, is y of t, is equal to a times e to the k times t.
00:26
So what we're going to do is we're going to use this first initial condition to find a.
00:33
What we need to do is we need to plug in 100 for y of t because, well, this is going to be y of 0 is equal to 100, which is also equal to a times e to the k times 0.
00:48
So, as we know, k times 0 is just going to be 0, and anything to the 0th power is just 1.
00:58
So what we end up with is a is equal to 100.
01:03
Now the next thing we need to do is we need to go to the second condition and solve for k.
01:10
So to do so, we plug in y of 2, which as we know is equal to 400...