For 1950, t = 0 and for 1990, t = 1980 - 1950 = 30
Given that the world population in the second half of the 20th century was modelled by the equation [tex]P(t) = 2560e^{0.017185t}[/tex].
The average world population during the time period of 1950 to 1980 is given by
[tex]Average\, world\, population= \frac{ \int\limits^{30}_0 {2560e^{0.017185t}} \, dx }{30-0} \\ \\ = \frac{2560e^{0.017185(30)}-2560e^{0.017185(0)}}{30(0.017185)} = \frac{2560(e^{0.51555}-e^0)}{0.51555} \\ \\ = \frac{2560(1.674559-1)}{0.51555} = \frac{2560(0.674559)}{0.51555} = \frac{1726.8717}{0.51555} =3,350\, million[/tex]
