Question

Population of a village increases every year by 2%,find the population after 2 years.if the present population is 40,000

Answer 1

AnswEr:-

Population after 2 years = 41,616

$\rule{200}{1}$

QuesTion:-

Population of a village increases every year by 2%.Find the population after 2 years if present population is 40,000.

Given :-

• Present population(P) = 40,000
• Increasing percentage (r) = 2%
• Time(n) = 2 years.

To find :-

• Population after 2 years = ?

${\underline{\dag\: {\frak{\bf\red{According \: to \: question \: :- }}}}}$

As we know,population increases in a compounded way.So after 2 years total population will be equal to componded amount after 2 years.

We know,

$\bf{\dag}\:\large{\boxed{\frak\blue{C.A. = P(1 + r)^n }}}$

• Putting all known values:-

$\twoheadrightarrow\sf A = 40,000(1 + 2\%)^2 \\\\\twoheadrightarrow\sf A = 40,000(1 + 0.02)^2 \\\\\twoheadrightarrow\sf A = 40,000(1.02)^2 \\\\\twoheadrightarrow\sf A = 40,000 \times 1.0404 \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\blue{A = 41,616 }}}}$

$\rule{100}{2}$

$\therefore\underbrace{\textsf{Population \: after \: 2 \: years = {\textbf{41,616 }}}}$

Answer 2

Answer:

$\frak{Given}\begin{cases}\textsf{Principal = 40,000}\\\textsf{Rate = 2\%\:p.a.}\\\textsf{Time = 2 years}\\\sf{Population_{(After\:2\:yrs)}=\:?} \end{cases}$

$\rule{160}{1}$

$\underline{\bf{\dag}\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:Amount = P \times \bigg(1 +\dfrac{r}{100}\bigg)^{t}\\\\\\\dashrightarrow\tt\:\:Population = 40000\times \bigg(1 +\dfrac{2}{100}\bigg)^{2}\\\\\\\dashrightarrow\tt\:\:Population = 40000\times \bigg(1 +\dfrac{1}{50}\bigg)^{2}\\\\\\\dashrightarrow\tt\:\:Population = 40000\times \bigg(\dfrac{51}{50}\bigg)^{2}\\\\\\\dashrightarrow\tt\:\:Population = 40000 \times \dfrac{51}{50} \times \dfrac{51}{50}\\\\\\\dashrightarrow\tt\:\:Population =16 \times 51 \times 51\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Population_{(After\:2\:yrs)} =41616}}$

⠀

$\therefore\:\underline{\textsf{Population of village after 2 yrs is \textbf{41616}}}.$