Question

The population of kansas city, missouri was 435,000 in 1990 and 482,300 in 2005. if the population is changing linearly, write an equation that gives the population p as a function of time, t. using the model determine the expected population in 2020.

Answer 1

Find the slope of the line connecting (1990,435000) and (2005,482300):

        482300-435000        47300
m = ----------------------- = ---------------- = 3153/yr (approx)
          2005 - 1990                15 yr

Use the point-slope formula to find the equation of this str. line:

y-435000 = (3153/yr)(x-1990)

The year 2020 is 30 years after 1990.  Thus, the expected pop in 2020 is

given by     y-435000 = 3153(30) = 94590, so that y = 529590.