00:01
The table gives the number of yeast cells in a culture.
00:03
So first we want to plot the data and estimate the carrying capacity of the yeast population, and round it to the nearest, and we want to round the nearest 10.
00:09
So we have our time and hours, and then our yeast cells.
00:13
We're going to plug that into a graphing calculator here in our table.
00:22
So we're plugging in time and hours from 0 to 18.
00:25
We're going up by 2s.
00:27
So 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18.
00:40
Then for our y column, that's the number of yeast cells.
00:43
So it starts with 17, then 37, 18, 171, 336, 509, 597, 640, 664, and then 67.
01:02
So let's plot those and see what they look like.
01:08
So we can see the modeling looks like a logistic curve.
01:13
It begins the rate of increase is increasing.
01:16
It's getting steeper and then it begins leveling out again.
01:19
So if we want to estimate the carrying capacity, that's what is this flattening out to? so we could drag this over here.
01:28
So we can see it's increasing and then it begins to level out the carrying capacity.
01:34
Capacity does and looks like it begins a level out at this last point here and we know that was at 672 we go back and look at our table so it looks like the carrying capacity if we rounded the nearest 10 is about 670 okay so next we're gonna use the first two points from the data to estimate the initial relative growth rate so it's talking about these two points here so the initial relative growth rate is just the difference in our yeast sales from these two times so that would be 37 minus 17 divided by the difference in time which could be 2 minus zero and that's going to give us 20 over 2 which would be 10 and that would be measured in sales per hour so initially it's growing about 10 cells per hour for those first two hours and next we want to find an exponential model for this data...