Math, asked by preetisaroj6533, 9 months ago

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

Answers

Answered by EliteSoul
330

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 }}}}


Anonymous: Awesome :)
Answered by Anonymous
173

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}}}.


Anonymous: Cool
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