Question

The population of Boulder County in 1995 was roughly 2.400×10^5. In 2005, it was more like 2.991×10^5. Assume (for this question) that the growth rate has been constant these 10 years, and will continue growing at this same rate indefinitely. How many years from 2005 will the population double from the 2005 level? Please provide with all the details and formulas.

Answer 1

if we plot this data on a graph, with population(x10^-5) on the y axis and year on the x axis,

according to the question, the slope will remain constant,

equation of line that passes through (1995, 2.4) and (2005, 2.991):

(y-2.4) = ((2.991-2.4)/(2005-1995))* (x-1995)

solving we get,

y = 0.0591x - 115.5045

to find the year in which population is 2*2.991*10⁵ = 5.982*10⁵

we put, y= 5.982, and solve for x

x=2055.6 (rounding off)

in the year 2055.6 population will be double as that in 2005

which is after 50.6 years from 2005