Park City, Utah was settled as a mining community in 1870 andexperienced growth until the late 1950s when the price of silverdropped. In the past 40 years, Park City has experiencednew growth as a thriving ski resort. The population data forselected years between 1900 and 2009 are given below.

Park City, Utah

Year	Population
1900	3759
1930	4281
1940	3739
1950	2254
1970	1193
1980	2823
1990	4468
2000	7341
2009	11983

(a) What behavior of a scatter plot of the data indicates that acubic model is appropriate?

a change in concavity and both a relative maximum and a relativeminimuma change in concavity and neither a relative maximum nor arelative minimum no change in concavity andan absolute maximumno change in concavity and an absoluteminimum

(b) Align the input so that

t = 0

in 1900. Find a cubic model for the data. (Round allnumerical values to three decimal places.)
p(t) =

(c) Numerically estimate the derivative of the modelin 2006 to the nearest hundred.

p'(106) =

(d) Interpret the answer to part (c).

In 2006, the population of Park City, Utahwas ---Select--- increasing decreasing ata rate of approximately people per year.