## Modeling Population

Every two years, the United Nations Population Division prepares estimates and projections of world, regional and national population size and growth. The estimated population of the world since 1950 is given in the table.

Year Year since 1950 World Population (billions)

1950 0 2.55

1955 5 2.8

1960 10 3

1965 15 3.3

1970 20 3.7

1975 25 4

1980 30 4.5

1985 35 4.85

1990 40 5.3

1995 45 5.7

2000 50 6.1

All the contents below are required to show on your presentation and slides (Includes plots, curve, graph, finite different table and related procedure).

A.

i. Use the data from the table to create a scatter plot on graph paper and by graphing softwares.(k,a) Draw a curve of good fit (k). Explain whether it is a function. (k,t,c)(B1.1)(15 p)

ii. Create a table of finite differences use the table of value (k,t), compare the equations and use the graph of each function to figure out what type of function is this (k,t)? (Linear, quadratic, or exponential). Evaluate its algebraic equation, show the procedure of evaluation (k,t,c).(B 2.1, 3.2) (25 p)

B. Determine

a) the domain and range,

b) real world restrictions,

c) y- intercept,

d) interval of increasing and decreasing

e) its asymptotes of the function

through the graph and algebraic expression (k,a).

State what properties result from its domain and range, y- intercept, interval of increasing and decreasing and its asymptotes (k,c). (B1.4, 3.2)(30 p)

C. Estimate the population size of year 2010 by finding value on the curve made by graphing software and tracing paper (k,t,a). And by using algebraic expression interpreting and patterning(k,t). Explain how the rational exponents affect the value(k,c). (B 1.2, 3.3)(20 p)

D. Search another set of data from the internet that can be modeled as an exponential function (k,a). Data can be found in Statistics Canada, E-STAT and etc. present your data by table of values and graph your data by graphing software(k,t,a). Explain why it is an exponential relation(k,c). Show your data and present your explanation(k,c). (B 3.1) (10 p)