Jared has opened a small online store selling hand-knit dog sweaters. and over the course of his first six months of business his sales revenues have steadily increased. In his first month of operation, he sold just $60 worth of sweaters, in his third month he sold $230 worth of sweaters, and in his sixth month he sold $535 worth of sweaters. Jared is not sure whether his revenues are growing linearly or not, and he wants to be able to make long-term forecasts. so he wants to explore various possible models to describe his revenues. In this proiect. you will explore various ways of modeling a function that passes through the points (1, 60), (3, 230), and (6, 535).Answer the questions below and then upload it for your instructor to grade. Follow the steps below: 1. Find a linear function (that is, a function of the form 3} = mm -I b for some constants m and bthat passes exactly through at least two of the three points (1, 50), (3, 230), and (6, 535). Is there more than one way to do this? Howr many different linear models are there that pass through at least two of the points? Use a graphing utility such as desmos.com to create a graph that shows all possible solutions on the same set of axes. Include the points (1, 60), (3, 230), and (6, 535) on your graph. 2. Find an exponential function (that is, a function of the form y = AB* for some constants A and B that passes exactly through at least two of the three points (1, 60), (3, 230), and (6, 535). Is there more than one way to do this? How many different exponential models are there that pass through at least two of the points? Use a graphing utility such as desmos.com to create a graph that shows all possible solutions on the same set of axes. Include the points (1, 60), (3, 230), and (6, 535) on your graph. 3. Find a power function (that is, a function of the form y = Cac for some constants C and & that passes exactly through at least two of the three points (1, 60), (3, 230), and (6, 535). Is there more than one way to do this? How many different power function models are there that pass through at least two of the points? Use a graphing utility such as desmos.com to create a graph that shows all possible solutions on the same set of axes. Include the points (1, 60), (3, 230), and (6, 535) on your graph. 4. Jared considers the possibility that his data might be growing quadratically. He assumes that if it is, the minimum of thefunction would be at (1, 60). Find a quadratic function that has its vertex at(]., 60) and also passes through at least one of the other two points. How many different quadratic models of this sort can you find? Use a graphing utility such as desmos.com to create a graph that shows all possible solutions on the same set of axes. Include the points (1, 60), (3, 230), and (5, 535)on your graph. Hint: you mayfind it easierto use \"vertex form"( y = A(:B h)2 -l '6] rather than "standard form" {y = Am2 -I- Ba: + C). 5. Last, Jared considers, as a worst-case scenario. the possibility that his data might be growing sinusoidally, with its minimum at (1, 60) and its maximum at (6, 535). Find a sinusoidal model (that is, a function of either the form 3; = :l:A sin(k(m 6)) + B that has these properties. Use a graphing utility such as desmos.com to graph your 3; = :EAcos(k(m c + B function. Include the points (1, 60), (3, 230), and(6, 535) on your graph. 6. Looking overall of the models you have found, which one seems to be the best fit for the data? Use the function you think is best to predict what Jared's revenue will be in his 8th month of operation