Question

the population of a city is 2000 what will its population be after 3 years if the rate of growth of world population is 10% per annum​

Answer 1

Answer:

Population after 3 years = 2000 + ( 2000 x 3 x 10/100)

= 2,000 + 600 = 2,600

Answer 2

Given :

• Present population = 2000
• Rate of increase = 10 %

To Find :

• Population after 3 years = ?

Solution :

$\bigstar$ Formula Used :

• ${\underline{\boxed{\red{\sf{ Population{\small_{(3 \; years)}} = Population{\small_{(Present)}} \bigg\lgroup 1 + \dfrac{Increase \; \%}{100} \bigg\rgroup^{Time} }}}}}$

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$\bigstar$ Calculating the Population after 3 years :

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = Population{\small_{(Present)}} \bigg\lgroup 1 + \dfrac{Increase \; \%}{100} \bigg\rgroup^{Time} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \bigg\lgroup 1 + \dfrac{10}{100} \bigg\rgroup^{3} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \bigg\lgroup 1 + \cancel\dfrac{10}{100} \bigg\rgroup^{3} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \bigg\lgroup 1 + 0.10 \bigg\rgroup^{3} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \bigg\lgroup 1.10 \bigg\rgroup^{3} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \times 1.10 \times 1.10 \times 1.10 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { Population{\small_{(3 \; years)}} = 2000 \times 1.331 } \\ \end{gathered}$

$\begin{gathered} {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\orange{\frak{ Population{\small_{(3 \; years)}} = 2662 }}}}}}}} \end{gathered}$

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$\bigstar$ Therefore :

❛❛ Population of the city after 3 years will be 2662 . ❜❜

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