 Hello and welcome to the session. In this session we will learn to identify linear function and exponential function using tables and graphs. Also we will recognize situations showing the linear relationship or exponential growth of the table. Now we start with identifying the function using table. Now we know that in a linear relationship there is a constant rate of change. That means a linear function wears our equal differences over equal inverters. For example let us see the following table. In this input output table we can see that change in x is constant that is 5 minus 0 is equal to 5 then 10 minus 5 is again 5 and 15 minus 10 is equal to 5. So the intervals are equal. So we can see that change in input values is constant. Now let us see change in output values given by y. Now here we can see 35 minus 30 is equal to 15 then 16 minus 45 is also 15 and 75 minus 16 is again 15. Thus the value of y is increasing by equal difference. So there is constant rate of change thus it is a linear relationship. Now let us see another table. Now in this table again we can see that change in x is constant that is 5 minus 0 is 5 then minus 5 is 5 and 15 minus 10 is also 5 so the intervals are equal. Now let us see the change in output values. Now here you can see y is also increasing that not by equal difference. Now here you can see 1,400 minus 1,000 is 200 then 1,440 minus 1,400 is 230 and 1,728 minus 1,440 is 288. So y is not increasing by equal difference therefore here the relationship is not linear. Now here we see the ratio of consecutive values of y that is 1,200 upon 1,000 which is equal to 1,2 then 1,440 upon 1,200 is away 1.2 and 1,728 upon 1,440 is also 1.2. So we can see that the ratio of consecutive values of y is constant thus it is an exponential function and this ratio is called factor. So exponential functions do not have constant rate of change but they have constant ratios. So we say that exponential function goes by equal factors over equal intervals. Now we can also identify the linear and exponential functions from graph. Now we know graph of linear function is a straight line that graph of an exponential function is a graph which is either increasing or decreasing and it does not intersect except this. Now here see the three graphs. Now the first graph is a straight line. So this graph shows a linear function and the second graph is an increasing graph. So it is exponential function showing growth and the third graph is decreasing graph so it is exponential function showing detail. Now we will recognize situations which show exponential growth or decrease or which show a linear relationship. Now consider the family statements. Statement 1 is given as a salesman company has following plan. It charges 59.95 dollars per month for 700 minutes and 0.25 dollars for each additional minute. Statement 2 is sales starts an experiment with 7500 bacteria cells. They increase by 30% every hour. After 4 hours there are 21,421 cells approximately. Now we have to identify the graph of relationship. Now see in statement 1 the salesman company charges fixed amount of 59.95 dollars per month for the first 700 minutes. Then it charges 0.35 dollars for each additional minute. Now we find its expression. It will be C is equal to 0.25 into M plus 59.95. Now this expression shows monthly cost of cost given by C. Repair charges will be 0.25 for M additional minutes plus 59.95 fixed charges. Clearly it shows a linear relationship with constant rate of change given by 0.25. So in statement 1 we have a linear relationship. Now in statement 2 we have given that bacteria cells increase by 30% every hour. So there is percentage growth rate now that X represents number of hours Y represents bacteria calculation. Now when X is 0 then we have initial calculation Y is equal to 7500. Now calculation is increasing by 30% every hour. So when X is equal to 1 then calculation that is Y is equal to 7500 plus 30% of 7500 That is equal to 7500 plus 30% of 100 into 7500 which is equal to 7500 plus now we have 75 into 30 is equal to 2250. Now adding we have 9750. So when X is equal to 1 then Y is equal to 9750. Now when X is equal to 2 then Y is equal to 9750 plus 30% of 9750. And on simplifying this is equal to 2675 by 1 X is equal to 3 then Y is equal to 2675 plus 30% of 2675. And on solving this is equal to 16477.5. Now when X is equal to 4 then Y is equal to 16477.5 plus 30% of 477.5. And on solving this is equal to 21420.75 which is approximately equal to 21421. So we see that after 4 hours there are 21421 cells approximately. So here we have obtained this input output table where X represents molecular parts and Y represents molecular population. Now it will be an exponential relationship. Now let us see the rate factor for consecutive values of Y. Now when we find ratio of consecutive values of Y we see that it is constant. So ratio is constant that is 1.3 plus we have same factor. So it is an exponential relationship thus in an exponential relationship the quantity varies and decays by a constant rate per unit interval related to another. In this session we have learnt how to identify linear and exponential functions using tables and graphs. And this completes our session. Hope you all have enjoyed the session.