Population problem

Algebra Level 4

The population of a country increases by 2% every year in the 20th century. What is

$\left \lfloor \frac { \text{Population at the end of the 20th century} } { \text{ Population at the start of the 20th century} } \right \rfloor = \ ?$

Notation: $\lfloor \cdot \rfloor$ denotes the floor function .

The answer is 7.

1 solution

Chew-Seong Cheong
Nov 6, 2017

The population $n$ years after is given by $A_n = A_0 (1+r)^n$ , where $A_0$ is the population at year 0 and $r$ is the annual rate of population growth. Therefore, for a century, we have:

$\begin{aligned} \left \lfloor \frac {A_{100}}{A_0} \right \rfloor & = \left \lfloor \frac {A_0(1+0.02)^{100}}{A_0} \right \rfloor = \left \lfloor \frac {7.245A_0}{A_0} \right \rfloor = \boxed{7} \end{aligned}$

Population problem

The answer is 7.

1 solution

0 pending reports