Park City, Utah was settled as a mining community in 1870 and experienced growth until the late 19505 when the price of silver dropped. In the past 40 years, Park City has experienced new growth as a thriving ski resort. The population data for selected years between 1900 and 2009 are given below. Park City, Utah Population 1970 1193 1980 2823 1990 4458 2000 7341 2009 11983 (a) What behavior of a scatter plot of the data indicates that a cubic model is appropriate? 0 a change in concavity and both a relative maximum and a relative minimum 0 no change in concavity and an absolute maximum 0 no change in concavity and an absolute minimum 0 a change in concavity and neither a relative maximum nor a relative minimum (b) Align the input so that t = 0 in 1900. Find a cubic model for the data. (Round all numerical values to three decimal places.) W) = (c) NumericallyI estimate the derivative of the model in 2007 to the nearest hundred P'(107) = (d) Interpret the answer to part (c). In 2007, the population of Park City, Utah was ---Select v at a rate of approximately :] people per year