Question

4, Shelby invests $700 in a bank account that earns a fixed 6% interest compounded annually. The amount in the account after t years is given by f(t) 700(1.06) a) Graph this function on your calculator in an appropriate window. Explain how you know this function has an inverse function. (Your answer should include complete sentences in contezt.,) b) Use this graph to sketch an accurate graph of the inverse function in an appropriate window. Label quantities and scales on both axes. c) What are the domain and range of the inverse function? (Your answer should include complete sentences in contert.) d) Pick one ordered pair on the graph of the inverse function (for which the value of the output is nonzero), and describe what it tells you about this context. (Your answer should include complete sentences in contezt.)

Answer 1

one one : - f(t_2) = f_1(t_2) implies t_2 = t_2 let t'_2 t_2 belongsto R consider f(t_2) = f(t_2) implies 700 (1.06)^t_2 = 700 (1.06)^t_2 or (1.06)^t_2 = (1 .06)^t_2 implies t_1 = t_2 onto: forall y belongsto R^+ exist t belongsto R s.t f(t) = y i.e forall y belongsto R^+ exist t belongsto R s.t f(t) = 700 (1.06)^t = y hence given function is one-one and onto therefore function has inverse domain of f^-1 = R^+ i.e f^_1: R^+ rightarrow R range of f^-2 = R let (t, t^-1(t)) be an orderderd pair then these ordered pair tells us in f^-2 (t) year we have t amount