Question

Complete the table shown to the right for the population growth model for a certain country.

Answer 1

The size of the population increases when the growth rate is positive and

decreases for a negative growth rate.

The completed table is presented as follows;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right]$

Reasons:

The table is presented as follows;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&\end{array}\right]$

The population in growth rate is given by the following formula;

P = a·(1 + r)ˣ

Where;

a = The initial population in 2003 = 40.5 million

P = The population in 2029 = 20.9 million

x = The number of years = 2029 - 2003 = 26

Therefore;

20.9 = 40.5 × (1 + r)²⁹

$\left (1 + r\right)^{29} = \dfrac{20.9}{40.5}$

$r = \left(\dfrac{20.9}{40.5} \right)^{\dfrac{1}{29} } - 1 \approx -0.02255$

The population growth rate is r ≈ -0.02255 = -2.255 %

The completed table is therefore;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right]$

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