 In this video we are going to compare the arithmetic and geometric growth in plants. So let's see what the differences are. Let's say here we have the tip of a plant and at the top of the tip there are these two yellow cells which are meristematic cells and as you know meristematic cells are cells that can divide. So these cells divide and each of these cells produced two cells in turn in let's say one hour. So in one hour each cell is dividing to form two cells. So then we have a total of four cells. Now only the top two cells will divide in the next hour and the bottom two cells won't. So again we will have an addition of two cells and then again an addition of two cells. So in arithmetic growth this is what happens every time a cell divides or let's say in a given amount of time the number of cells added the number of new cells added remains constant. In this case two cells are being added every hour. In geometric growth it's a little bit different. How is it different? We can see this with bacteria as well as plants so let's look at bacteria. So let's say we start with two bacteria in geometric growth what happens is both of the cells will divide and let's say in this case each cell will divide to form two cells. So each of the cells give rise to two more cells so two cells are added right so initially we had two cells and then two cells give rise to four cells. So each time the number of cells double because each cell can give rise to two cells every time they divide. So let's say in one hour every cell doubles. So in the first hour two cells form four cells and then in the second hour what will happen is four cells will form eight cells. So notice what's happening to the number of new cells being added. In the first instance we had two cells added in the second instance we had four cells that were added and then next we will have eight cells that are added. So each time the number of new cells that are added is doubling whereas in case of arithmetic growth each time the number of cells that were added was constant two. In this case it started with two then it became four then it became eight. So that is a fundamental difference between arithmetic growth and geometric growth. The number of new cells added in arithmetic growth per unit time remains the same whereas in geometric growth it increases. Now let's take a look at the formulas representing the two growths. In arithmetic growth the formula is nt is equal to n0 plus rt. So what are these different things? nt is the number of cells at a given time. So let's say number of cells at time t. This is nt and what is n0? n0 is the number of cells at time 0. Then what is r? r is the growth rate constant. This is a constant for the type of growth that we are looking at and where we are looking at. Let's say in this particular case this plant it is some value in some other plant it will be some other value. So r differs from plant to plant or organism to organism and then t is time. Now let's take a look at geometric growth formula. So in geometric growth we have nt is equal to n0 times e to the power rt. nt and n0 are the same. nt is the number of cells at time t. n0 is the number of cells at the beginning. r is again the growth rate constant and t is the time. e is something that is not there in arithmetic growth formula. e is an irrational constant or irrational number which is a constant and this is a very important number in mathematics and it's used in a number of calculations and its value is 2.718 and it goes on like this. So since we have an exponent this is an exponent that is why geometric growth is also called exponential growth. Now let's take a look at the graphs of the different types of growth. So what we'll do is we will plot nt versus time. In arithmetic growth we see a straight line and hence since it's a line a straight line this type of growth is also called linear growth and in geometric growth what do we see? We see this type of a graph. So you see the difference in linear growth the slope of the line remains constant whereas in geometric growth the slope of the curve keeps changing in fact it starts off at a low slope where the graph is rising slowly and then it rises faster and faster which means the slope keeps increasing. So we've seen that in arithmetic growth the number of cells that are added per unit time is constant whereas in geometric growth the number of cells that are added per unit time increases with time. The formula of arithmetic growth is given by nt is equal to n0 plus rt whereas the formula for geometry growth is given by nt is equal to n0 e to the power rt and because there is an exponent involved geometric growth is also called exponential growth and in arithmetic growth the graph is a straight line hence it's also called linear growth and in geometric growth the graph looks like this where the slope keeps increasing with time.