The population of Mexico between 1921 and 2010 can be modeled as
p(t) = 8.028e0.025t million people
where t is the number of years since 1900.†
(a) What was the population of Mexico in 2006? (Round your answer to three decimal places.)
How rapidly was the population of Mexico growing in 2006? (Round your answer to three decimal places.
(b) Write a linearization of p in 2006. (Round all numerical values to three decimal places.)
pL(t) =
(c) Use the linearization to estimate the population of Mexico
in 2013. (Round your answer to three decimal places.)
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Answer:
Years since 1900 = 106
a)
P(106) = 8.028e^0.025*106 = 113.628 Million
b)
P'(t) = 8.028*0.025*e^(0.025*t) = 0.2007*e^(0.025*t) = 2.841 million/yr
c)
t = 2013 - 1900 = 113
Pl(t) = p(106) + p'(106)*(t-106)
= 113.628+2.8407*7 = 133.513 million people
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