In 1996 the population of Russia was 148 million and the population of Nigeria was 104 million. If the populations of Russia and Nigeria grow at annual rates of -0.62% and 3.0%, respectively, when will Nigeria have a greater population than Russia?

Algebra 2

1 Answer
Jul 19, 2018

2006

Explanation:

We can express these as exponential growths and decays.

For each, we have the following functional form
P = P_0 (1+g)^t
where
P is the population at time t
P_0 is the initial population
g is the growth rate, e.g. -0.0062 or 0.03
t is the number of years which have passed.

We can set these up for both populations and set them equal to eachother:
P_R = P_N
P_(R,0) (1+g_R)^t = P_(N,0) (1+g_N)^t
148 (1-0.0062)^t = 104 (1+0.03)^t
148/104 = (1.03/0.9938)^t
t = ln(148/104) /ln(1.03 / 0.9938) = ln(1.4231)/ln(1.036) = 9.976

So before 2006, Nigeria will outpace Russia in population