According to the CIA’s World Fact Book, in 2010, the population of the United States was approximately 310 million with a 0.97% annual growth rate. (Source: www.cia.gov) At this rate, the population P(t) (in millions) can be approximated by P(t) = 310(1.0097)t, where t is the time in years since 2010.
a. Is the graph of P an increasing or decreasing exponential function?
b. Evaluate P(0) and interpret its meaning in the context of this problem.
c. Evaluate P(10) and interpret its meaning in the context of this problem. Round the population value to the nearest million.
d. Evaluate P(20) and P(30).
e. Evaluate P(200) and use this result to determine if it is reasonable to expect this model to continue indefinitely.
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