00:01
So the first clue that this function is following from exponential is i'm just going to do a times b to the x.
00:07
I believe that's the only thing you can use for the situations that at the culture is 200 at 15 minutes.
00:18
And then again at 30 minutes, it was 1700.
00:27
So what you can do is start plugging into this problem like a times b to the 15th power needs to equal 200.
00:34
And then also a, i need it, the times in there, b to the 30th power would equal 1 ,700.
00:42
And what i do, at least this is what i do, is just divide the b to the 15th power over, and also on this one, divide the b to the 30th power over.
00:54
And the thought process is both these equal a, so they must equal each other.
00:59
And usually what i do is just multiply the higher exponent to the left side.
01:04
So b to the 30th is being multiplied to the left side.
01:10
And the reason for that, i guess i could have also divided the 200 over that might actually make the math a little bit easier is when you're dividing with the same exponent, you subtract, sorry, dividing with the same base, you subtract the x one as 30 minus 15 is 15.
01:27
And what you can do is take this to the 115th power and i would use a calculator because i have no idea what that is.
01:40
17 halves to the 115th hour.
01:45
You might need to put this in parentheses.
01:47
But anyway, you get 1 .15335.
01:52
I think you'll stop right there as the base.
01:56
I forgot to write that.
01:58
There we go.
01:58
So that's the base value, which is only helpful to figure out the a value.
02:03
And i'm going to leave it in my calculator as the answer to the 15th power, and i'll get the best answer for a.
02:13
So 200 divided by my answer to the 15th power is an initial population of 23 .529.
02:26
So that's the initial, which they ask for...