The table gives the population of the world P(t), in millions, where t is measured in years and t = 0 corresponds to the year 1900.
t  Population (millions) 

0  1650  
10  1750  
20  1860  
30  2070  
40  2300  
50  2560  
60  3040  
70  3710  
80  4450  
90  5280  
100  6080  
110  6870 
(a) Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant fines.
(b) Use a graphing device to find a cubic function (a third degree polynomial) that models the data.
(c) Use your model in part (b) to find a model for the rate of population growth.
(d) Use part (c) to estimate the rates of growth in 1920 and 1980. Compare with your estimates in part (a).
(e) Estimate the rate of growth in 1985.
Part (a)
To estimate: The rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.
1) Formula:
2) Calculation:
First calculate rate of population growth in 1920.
So, first find slope for secant line between 19101920 and 19201930. Then find average between them.
Do same process for 1980.For 1920
Part (b)
To find: a cubic function that models the data.
Part (c)
To find: a model for the rate of population growth.
Part (d)
To estimate: the rates of growth in 1920 and1980.
To estimate: the rate of growth in 1985.
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