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Over a period of 20 years, the population P (in thousands) of a town can be modeled by
P=0.0081³-0.245² +2.13t+ 95.8
where is the time (in years).
a. Use a graphing calculator to graph the function for the interval 1 << 20. Describe the behavior of the graph on this interval.
From
decreased.
and from
the town's population increased. From Year
The average rate of change was about thousand people per year.
b. What was the average rate of change in the town's population from Year 1 to Year 20? Round your answer to the nearest tenth.
c. Use the model to predict the town's population in Year 25. Round your answer to the nearest tenth.
Population in Year 25: thousand people
d. Why should the model not be used for many years after Year 20?
to Year
O The model population approaches negative infinity as the year approaches infinity.
the population
O The model population approaches infinity as the year approaches infinity
O The model population stays the same as the year approaches infinity