The numbers N of confirmed cases of Lyme disease in Maryland from 2007 through 2014 are shown

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The numbers N of confirmed cases of Lyme disease in Maryland from 2007 through 2014 are shown in the table, where t represents the year, with t = 7 corresponding to 2007. (Source: Centers for Disease Control and Prevention)
The numbers N of confirmed cases of Lyme disease in
DATA Year, t Number, N 2576 8. 1746 1466 10 1163 11 938 12 1113 13 801 14 957 Spreadsheet at LarsonPrecalculus.com

(a) Use a graphing utility to create a scatter plot of the data.
(b) Use the regression feature of the graphing utility to find a quartic model for the data. (A quartic model has the form at4 + bt3 + ct2 + dt + e, where a, b, c, d, and e are constant and t is variable.) Graph the model in the same viewing window as the scatter plot.
(c) Use the model to create a table of estimated values of N. Compare the model with the original data.
(d) Use synthetic division to confirm algebraically your estimated value for the year 2014.

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