 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Joseph put $450 under his mattress and also deposits $600 in a bank with a 4% interest compounded annually. Write an equation to represent the total amount of money Joseph will have at time t show how the base and vertical shift are displayed in the function. Now let us start with the solution of this question. See this problem deals with the interest that is compounded annually and we need to write an equation that represents the total amount of money Joseph will have at time t let us first find the amount of money Joseph will have in the bank after t years we are given that he deposited an initial amount of $600 in the bank thus A will be equal to $600 the interest on this amount is 4% which is compounded annually since the amount of money will increase with interest so the growth factor B is given by 1 plus R where R is percentage rate thus we can say that growth factor is equal to 1 plus R which is given as 4% and this is equal to 1 plus 4 by 100 and this is equal to 1 plus 0.04 which can be written as 1.04 so base B or growth factor B is equal to 1.04 we know that amount after t years when interest is compounded annually at the rate R% is given by A into 1 plus R% whole raise to part t thus the expression is y is equal to A that is the initial amount that is $600 into 1 plus R% whole raise to part t which is given by 1.04 raise to part t also he has total $450 under his mattress so the total amount Joseph will have at time t is given by y is equal to 450 plus 600 into 1.04 raise to part t this equation is of the form y is equal to A into B raise to part t plus K where K is the vertical shift so here the vertical shift is of 450 and base B is given by 1.04 which is the required answer this completes our session hope you enjoyed this session