The following table gives the percent of adult Americans with diabetes for selected years from 2010 and projected to 2050.
(a) Find a logarithmic function that models the data, with x equal to the number of years after 2000 and y equal to the percent of the adult American population with diabetes. Report the model with three significant digits.
(b) Use the reported model to find the instantaneous rate of change of the percent of Americans with diabetes.
(c) At what rate is the percent of Americans with diabetes projected to increase in 2030?

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