 Let's look at arithmetic growth in plants. Let's say we have a plant. This is the tip of a plant, tip of the stem of a plant and here if you see the two cells in yellow, these belong to meristematic tissue and you might recall that meristematic tissue is made of cells which can divide. So these cells divide because they can and they want to and they form two more cells. However after that the bottom two cells in the meristematic tissue they divide, they decide that we don't want to divide anymore. So they stop dividing but the top two cells they are like okay we can still divide. So they go ahead and divide and form two more cells. And now these two cells again stop dividing and the top two cells divide again and this goes on and on. So if you notice every time the cells divide two new cells are added. So how do we quantify all this? Let's try doing that and see if we can find any formula for the phenomenon that is happening over here. So let's say each division each time the cells divide it happens every hour. So in one hour two cells are added. So if in one hour two cells are added, how many cells will be added after three hours? Naturally two times three right which is equal to six. Now if I were to ask you what is the total number of cells after three hours? So in order to find that you have to remember that we started off with two cells in the beginning. So two plus in the three hours we added two times three cells. So two plus two times three which is two plus six which is equal to eight cells which is exactly what we see over here. There are eight cells. Now let's take a little bit different scenario. Let's say now we start with ten cells and let's say after two hours five cells are added. Then after one hour how many cells will be added? Five by two right which is equal to 2.5 cells. Of course 2.5 cells don't really mean anything but we calculate this just for the sake of simplicity because it's easier to calculate things if we follow the unitary method. So now let's say we want to find out after six hours how many cells are added. We don't want to sit and count. We just want to use mathematics to find that out. And since we've already found out in one hour 2.5 cells are added for six hours we have 2.5 times six is equal to 15 cells that are added. Now if I were to ask you again what is the total number of cells we started out with 10 cells. So first take that then add whatever we calculated over here which is 2.5 times 6 which is equal to 15 plus 10 25 cells. So we have 25 cells in the end. Now let's see if we can choose these two scenarios and find out a formula. Let's say we want to find out the total number of cells after a given amount of time. For any system it can be any plant with any amount any number of cells that are added per hour or per minute or whatever it is. So let's say I want to find out NT where N is the number of cells and T is the time. So at a given time how many cells are there? We want to find that out. So how do we do that? Let's look at the calculations that we adjusted for these two different cases. So NT is equal to so in both cases you see we start we first write the initial number of cells that were there in this case 2 and in this case 10. So let's say the initial number of cells is N0 N is again the number of cells and 0 is when time started when we started counting the time and then what do we add? We add whatever number of cells were added. So what were added? Over here is 2 times 3 over here it's 2.5 times 6. So let's see first if there is any similarity 2 is the number of cells added in an hour. What about 2.5 here? Again it's the number of cells added per hour. So that's the rate that is the number of cells added per hour. It's called the growth rate constant and then what is this last number here? Over here it's 3 and over here it's 6. Remember that's the time that we were we wanted to find out the number of cells for. So that will be T. So this is the general formula for this type of growth. It's NT is equal to N0 plus RT and this type of growth is called arithmetic growth. Now let's see what the graph looks like. So what do we plot over here? We plot NT the number of cells at a given amount of time and the time in hours. So first remember at zero time we'll take the first case so at zero time in the first case there were two cells. So we plot two over here and then after the first division was done that is after one hour we had four cells and then after two hours we had six cells and then after three hours we had eight cells. So if we were to join the dots what do we see? We get a straight line because we get a straight line. This type of growth is also called linear growth. So we have seen that in arithmetic growth or linear growth this is the formula that we can use to find out the number of cells in a given amount of time provided we know the growth rate constant which is nothing but the number of cells added per unit time and if we plot the graph of growth we see a straight line.