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The table gives the world population P(t), in millions, where t is measured in years and t = 0 corresponds to the year 1900.
Population (millions) Population (millions) 1650 60 3040 10 1750 70 3710 20 1860 80 4450 30 2070 90 5280 40 2300 100 6080 50 2560 110 6870
(a) Estimate the rate of population growth in 1920 and in 1980 by averaging the slopes of two secant lines.
(b) Use a graphing calculator or computer 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) In Section 1.1 we modeled P(t) with the exponential function f (t) = (1.43653 × 109) · (1.01395)t
Use this model to find a model for the rate of population growth.
(f) Use your model in part (e) to estimate the rate of growth in 1920 and 1980. Compare with your estimates in parts (a) and (d).
(g) Estimate the rate of growth in 1985.
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