Question

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

Answer 1

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