Projections indicate that the percent of U.S. adults with diabetes will dramatically increase. The table gives the percent of U.S. adults with diabetes for selected years from 2010 and projected to 2050.

(a) Find a logarithmic model, y = f (x), for these data. Use x as the number of years after 2000.

(b) Find the function that models the rate of change of the percent of U.S. adults with diabetes.

(c) Find and interpret f (25) and f'(25).

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Year Percent Year Percent 2010 15.7 2035 29.0 2015 18.9 2040 31.4 2020 21.1 2045 32.1 2025 24.2 2050 34.3 2030 27.2