Mathematics - Linear Operators
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The U.S. Census Bureau International Database gives the population of the ten most- populated countries in the year 2000 and population predictions for 2050 for these countries: Chinahad 1.2 billion people in 2000 and is
predicted to have a population of 1.3 billion in 2050. The U.S. had a population of 284 million in 2000 with a prediction of 420 million by 2050.
a. Assuming exponential population growth, predict the populations of China and the U.S. in the years 2100 and 2200.
b. Assuming exponential population growth, approximately when will China's population double?
c. What factors might make the assumption of exponential growth a faulty assumption?
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(a) (i) China:
Let the population growth model be P(t) = P(0) e^kt
By using the data and taking year 2000 as t = 0, we have P(t) = 1.2 e^kt
When t = 50, P(50) = 1.2 e^(k * 50) = 1.3
e^(50k) = 1.3/1.2 = 1.0833
50k = ln 1.0833
k = 0.0016
The model is P(t) = 1.2 ...
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