 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Lisa and Jane tried to get a monthly allowance from their mother if their mother initially gave them a cent and two cents for the first day of the month four cents for the second day, eight cents for the third day and so on. How much would their mother have to pay on the tenth day of the month? Sketch the graph of the relationship between the two quantities and explain what does the point with coordinates 01 represent? Now let us start with the solution of the given question. We are given that Lisa and Jane get a monthly allowance from their mother. Their mother initially gave them a penny, then on the first day she gave them two cents, on the second day she gave them four cents and on the third day she gave them eight cents and so on. Let us draw its table. In the first column we write the days which is represented by variable x and in the second column we write cents given by their mother, represented by variable y. We are given initially she gave them one cent so when x is 0, y is equal to 1. On first day of the month she gave two cents so when x is equal to 1, y is equal to 2. Similarly when x is equal to 2, y is equal to 4. When x is equal to 3, y is equal to 8. Now we shall find a pattern. We can write 1 as 2 raised to power 0, 2 as 2 raised to power 1, 4 as 2 raised to power 2 and 8 as 2 raised to power 3. So we say that it is an exponential function whose equation will be y is equal to 2 raised to the power x. Now we have to find how much would their mother have to pay on the 10th day. So here we put x is equal to 10 in this equation and we get y is equal to 2 raised to the power 10 which implies that y is equal to... Now using calculator we find the value of 2 raised to the power 10 and this is equal to 1024. So y is equal to 1024 thus their mother will pay them 1024 cents or we can call it as 10.24 dollars. Now let us graph this relationship. We plot these points given in the table on coordinate plane. Now here we have plotted the points with coordinates 0, 1, 1, 2, 2, 4 and 3, 8 and we have joined these points forming an exponential curve. This is the required graph which shows an exponential relationship between the two quantities. Now the point with coordinates 0, 1 is the y-intercept. It represents that before the starting of the month that is when x is equal to 0 their mother gave them 1 cent. This is the required answer. This completes our session. Hope you enjoyed this session.