Question textIn 2014, Tom took most of his savings ($6,000) and invested it in a managed fund which is based on cash, shares and real estate investments. Tom received the following summary of the yearly value of his investment in a recent statement - consider this to be the original set of data. The year data can be converted to represent the number of years since the initial investment - consider this to be the adjusted set of data. years = np.arange(2014, 2025) balance = np.array([6000, 6495.65, 7690.43, 8155.08, 8900.29, 9996.97, 11941.28, 12598.42, 14264.11, 17930.75, 20596.31])num_years = years - years[0] a) Fit a linear model (\(y=a_0+a_1x\)) using the original set of data. \(a_0\): Answer 1 Question 1[input] (0 decimal places)\(a_1\): Answer 2 Question 1[input] (0 decimal places) b) Then, fit a linear model (\(y=a_0+a_1x\)) using the adjusted set of data.\(a_0\): Answer 3 Question 1[input] (0 decimal places)\(a_1\): Answer 4 Question 1[input] (0 decimal places) c) Fit a power law model (\(y=\alpha x^{\beta}\)) to the original set of data. \(\alpha\): Answer 5 Question 1[input] (2 decimal places)\(\beta\): Answer 6 Question 1[input] (0 decimal places) d) Fit a power law model (\(y=\alpha x^{\beta}\)) to the adjusted set of data. \(\alpha\): Answer 7 Question 1[input] (0 decimal places)\(\beta\): Answer 8 Question 1[input] (4 decimal places) e) Fit an exponential model (\(y=\alpha e^{\beta x}\)) to the original set of data. \(\alpha\): Answer 9 Question 1[input] (2 decimal places)\(\beta\): Answer 10 Question 1[input] (4 decimal places)f) Fit an exponential model (\(y=\alpha e^{\beta x}\)) to the adjusted set of data. \(\alpha\): Answer 11 Question 1[input] (0 decimal places)\(\beta\): Answer 12 Question 1[input] (4 decimal places)多项填空题