Posted: November 2nd, 2022

The graph of a function () passes through the points

1. The graph of a function () passes through the points (2 , −1), (−1, 11), (−2, 27) and (1, 3).(a) Find a Cubic polynomial () = 3 + 2 + + whose graph passes through thesepoints using matrices. Hint: Setup a Systems of Equations for each of the ordered pairs andthen solve for the unknowns.(b) Graph () . Show the equation of the trend-line (Cubic Polynomial) on thegraph.2. Carpet City wants to develop a means to forecast its carpet sales. The store manager believesthat the store’s sales are directly related to the number of new housing starts in town. Themanager has gathered data from county records on monthly house construction permits andfrom store records on monthly sales. These data are as follows:Carpet5 1043821211914Sales(000 yd.)Permits21 35101216941151826Develop a linear regression model using Data Analysis (Regression) for these data and forecastcarpet sales if 30 construction permits for new homes are filled.3. The surface roughness of coated interior pipes (in micrometers) used in oil fields is as follows:1.72, 2.50, 2.16, 2.13, 1.06, 2.24, 2.31, 2.03, 1.09, 1.40, 2.57, 2.64, 1.26, 2.05, 1.19, 2.13, 1.27,1.51, 2.41, 1.95.(a) Find the sample mean and the sample standard deviation.(b) Construct a 95% confidence interval for the population mean by using the followingequations: = ̅ −√and = ̅ +.√594. The equation = ( − 32) ∗ + 273.15 coverts the temperature from ℉ (Fahrenheit) to K(Kelvin) and vice versa. Create a macro to convert temperature from K to ℉. Name the macroKTOF (Keyboard shortcut: Ctrl + k). Use KTOF to convert 233.15, 273.15, 288.70, and 310.93to℉. Your solution should clearly show the macro.5. Compound interest is given as = (1 + ) where A is the amount (future value) at the endof n periods, P is the principal (present value), i is the interest rate per compounding period, andn is the number of compounding periods.A newborn child receives a $20,000 gift toward college from her grandparents. If the money isinvested at 7% compounded quarterly, write a VBA function (Name it FVAL) to find the futurevalue in 17 years by using the equation given above.Create a second VBA function (Name it TINT) to find the total interest that will be paid over 17years.Use FVAL and TINT to find the future value and the total interest for 19 years, 21 years, 23 years,and 25 years. Your solution should clearly show the functions.

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