Question

In 2001 the world’s population was 250000. With a growth rate of approximately $14\%$. What was the population in 2011?

Answer 1

Here we have given the initial population, growth rate, and the number of years after which we have to find the population. Substitute the values in the formula $A{\left( {1 + \dfrac{r}{{100}}} \right)^n}$ to find the population in 2011.

Formula Used: If A is the initial population and B is the population after n period of time (in years) with a growth rate of $r\%$, then we can write the formula for the population as $B = A{\left( {1 + \dfrac{r}{{100}}} \right)^n}$.

Complete step by step answer:
We are given the initial population in 2001 as 250000.
$\Rightarrow A = 250000$
The rate of growth is given 14%.
$\Rightarrow r = 14\%$
The time period from 2001 and 2011 is,
$\Rightarrow n = 2011 - 2001$
Subtract the values on the right side,
$\Rightarrow n = 10$
Substitute these values in the formula of the population,
$\Rightarrow B = 250000{\left( {1 + \dfrac{{14}}{{100}}} \right)^{10}}$
Calculate the value inside the bracket by taking LCM
$\Rightarrow B = 250000{\left( {\dfrac{{100 + 14}}{{100}}} \right)^{10}}$
Add the terms in the bracket,
$\Rightarrow B = 250000{\left( {\dfrac{{114}}{{100}}} \right)^{10}}$
Divide the numerator by the denominator,
$\Rightarrow B = 250000{\left( {1.14} \right)^{10}}$
Simplify the term,
$\Rightarrow B = 250000 \times 3.70722$
Multiply the terms,
$\therefore B = 926805$

Hence, the population in 2011 is approximately 926805.

Note: Students are likely to make mistakes in substituting the value of r as 0.14 as it is given in percentage form. Keep in mind when the formula has $\dfrac{r}{{100}}$ then we substitute only the numeric part of the percentage, else we convert the percentage into fraction or decimal and then substitute. Also, while performing the complex calculations, move step by step to avoid calculation mistakes.
Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.