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Population of Southberg Town

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January 22nd, 2023

The population of the town of Southberg can be modeled by the function:
P(t) = t^4 – 18t^3 + 77t^2 + 69t + 6405 for 0 < t < 20 where t is in years and t = 0 corresponds to the year 1991.

a) What was the population of the town in the year 2002?
b) What was the population of town in year 2011?
c) What was the instantaneous rate of change of the population of town in year 1996?
d) What was the instantaneous rate of change of the population in year 2011?
e) Use your previously stated answers to this problem to estimate the populate of Southberg in the year 2012.

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