3. The United Nations\' world\'s addition of 78 million people.\" Department of

Question

3. The United Nations' world's addition of 78 million people." Department of Economic and Social Affairs stated in 1999 that "the stands at 6 billion and is growing at 1.3% per year, for an annual net Economic a. This statement contains two descriptions of predicting world population growth that tdct each other. What are the two descriptions and why are they contradictory? b. Usi ng the information in the statement, construct a linear model for world population in billions in terms of years from 1999. Define your variables. Using the information in the statement, construct an exponential model for world population in billions in terms of years from 1999. Define your variables. c. d. Complete the table for the two models you have constructed Years Years from 1999 1999- 2000 2001. 002 200512010 Popuo fiom inear mocdel (billions) Population from exponential model (billions e. In your table, you should see that the models have the same prediction for two years What are the two years and why is this the case? (If you don't see this, check your work. If you turn in this homework and you have not done this check, your work will be returned to youl) Which model predicts larger populations after the year 2000? Why does this make sense? f.

Explanation / Answer

a)

one model suggests that the population is increasing 1.3% every year which means if in year 1 the population is P (in year 1), then next year (year 2), it will become 1.013 P. and 2 years after it will increase 1.3% on the last years base (year 2)

while the other model takes constant increase of 78 million every year, which can not be same as last model where increment is changing every year.

b)

P(t) = 6 + 0.078 t

c)

P(t) = 6(1.013)^t

d)

year 1999 2000 2001 2002 2005 2010 t (yrs after 1999) 0 1 2 3 6 11 linear model pop 6 6.078 6.156 6.234 6.468 6.858 exp model pop 6 6.078 6.157014 6.237055 6.483476 6.916003

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