The following table gives the projected population, in thousands, of Americans over 100 years of age.
(a) Create an exponential function that models the projected population y, in thousands, as a function of the number of years past 2010. Report the model with three significant digits.
(b) Use the reported model to find a function that gives the rate of change in the projected number of centenarians.
(c) What is the projected rate of change in the number of centenarians in 2040?

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Centenarians Centenarians Year (thousands) Year (thousands) 2015 2040 2045 78 230 2020 106 310 2025 143 2050 442 168 2030 2055 564 2035 188 2060 690