Question

In 2017 population of country X was 95.5. The population growth rate between 1990-2017 was 0.0126 (1.26%) per year. What was the population of country X in 1990?

Answer 1

The population of country X in 1990 is 68.105

Problem Statement

The question tells us that the population growth rate of a country from 1990-2017 was 1.26%. We are asked to calculate the population of the country in 1990 given that the population in 2017 is 95.3.

Method

In order to solve this question, we need to apply this formula:

`\begin{gathered} P_2=P_1(1+r)^t \\ \text{where,} \\ P_1=\text{ Initial population} \\ P_2=\text{ Final population} \\ r=\text{rate of growth of population} \\ t=\text{time between the two populations} \end{gathered}`

Let us list the parameters given in the question:

`\begin{gathered} P_2=95.5\text{ (2017 population)} \\ P_1=\text{? (1990 population)} \\ r=1.26\text{ \%}=(1.26)/(100) \\ t=2017-1990=27\text{ years } \end{gathered}`

Now that we have the parameters and know what term in the formula we need to find, we can apply the formula.

Implementation

`\begin{gathered} P_2=P_1(1+r)^t \\ 95.5=P_1(1+(1.26)/(100))^(27) \\ 95.5=P_1*(1.0126)^(27) \\ 95.5=P_1*1.402245 \\ \text{Divide both sides by 1.402245, we have:} \\ P_1=(95.5)/(1.402245)_{} \\ \\ \therefore P_1=68.105 \end{gathered}`

Final Answer

The population of country X in 1990 is 68.105

Here are the screenshots of the solution: