 Hello and welcome to the session. In this session, we will interpret the parameters in a linear or exponential functions in terms of a context. That is, we will master the following scales. We will interpret the slope and x and y intercepts in a linear function in terms of a context. We will interpret the base value and vertical shift in an exponential function of the form f of x is equal to v raise to power x plus k where b is an integer and k can be equal to 0. We will also interpret the base value and initial value in an exponential function of the form f of x is equal to a into b raise to power x where b is an integer and a can be any positive integer including 1. Now, let us see an example. In this example, we are given that any is picking apples with her sister. The number of apples in her basket is described by n is equal to 22t plus 12 where t is the number of minutes and he spends picking apples. What are the numbers 22 and 12 tell you about any's apple picking? Now, in this example, we have to interpret the parameters given by 22 and 12. We are given the linear relationship by equation n is equal to 22t plus 12 where n is the number of apples and t is the time spent by any in picking up the apples. Now, this equation is of the form y is equal to n x plus b which is slope intercept form of the equation where m is the slope and b is the y intercept. Now, let this be equation 1 and this be equation 2. So, comparing equation number 1 and 2, we have m is equal to 22 and b is equal to 12. So, this is the slope and this is the y intercept. Now, we know that slope tells us the rate per unit and intercept gives us the initial value thus 23 tells us the rate at which any is picking up the apples per unit. And 12 tells us that initially she started with 12 apples. Now, let us interpret the parameters in exponential functions. Now, let us see one example. Now, in this example, we are given that Ben earned $1600 last summer. He deposited the money in a bank account that earns 6% interest compounded annually. Now, see this problem deals with the interest that is compounded annually. This means that each year the interest is calculated on the amount of money Ben had in the bank. That interest is added to the original amount and next year the interest is calculated on this new amount. In this way, we get paid interest on the interest. Now, we will write the function that describes the amount of money in the bank. Here, the general form of an exponential function will be y is equal to a into b raised to power x where y is the total amount of money In the bank, x is the number of years from now and a will be the initial amount that Ben deposited in the account. Now, we know that weight of interest 6% per year since the amount of money will increase with interest. So, growth rate b is 1 plus r the whole where r is the percent weight. So, growth rate is equal to 1 plus 6% that is equal to 1 plus 6 upon 100 which is equal to 1 plus 0.06 That is equal to 1.06. So, b is equal to 1.06. Also, initial amount a is given as $1600. So, a is equal to $1600. Now, we will put the values of a and b in this equation and we get y is equal to $1600 into $1.06 raised to power x. We have written the function that describes the amount of money in the bank and here the initial amount that is a is equal to $1600 and growth rate b is equal to $1.06. Now, consider the exponential function of the type y is equal to b raised to power x plus k where b is an integer and k can be 0. Now, in this equation, vertical shift is given by k. Now, suppose we have equation of type y is equal to 2 raised to power x plus 5. Now, here vertical shift given by k is equal to 5 and rate factor which is given by b is equal to 2. Now, let us see this with the help of graph. Now, here we have drawn two curves. Red curve is the graph of the equation y is equal to 2 raised to power x and blue curve is the graph of the equation y is equal to 2 raised to power x plus 5. Now, both curves have same rate factor 2 but both intersect at different points on vertical axis. Red curve intersects the vertical axis at the point 0, 1 and blue curve intersects the vertical axis at the point 0, 6. Thus, when we shift the red curve 5 points up, we will get the blue curve. So, this is the vertical shift. So, for the equation of the type y is equal to 2 raised to power x plus 5, 5 represents vertical shift and 2 represents rate factor. So, in this session we have interpreted the parameters in a linear or exponential function in terms of a context and this completes our session. Hope you all have enjoyed the session.