Question

the population of a village is 5000 and it increases at yeh rate 2% every year. after 2 years the population will be​

Answer 1

$\huge{\text{\underline{Correct\; Question:-}}}$

The population of a town increases every year by 2% of the population at the beginning of that year. The number of year by which year the total increase of population be 40% is

$\huge{\text{\underline{Solution:-}}}$

Let us assume that the initial population as P

★ Now after a year population will be:-

$\implies$ P + (2 / 100) P

$\implies$ P (102 / 100)

$\implies{\boxed{\text{1.02 P}}}$

★ Similarly after 2 years population will be:-

$\implies$1.02 x 1.02 x P

★ So after n number of years population will be:-

$\implies{\tt{P x (1.02^n)}}$

★ Point to remember:-

Now this population should be equal to P + 40%

$\implies{\tt{1.4 P = P x (1.02^n)}}$

$\implies{\tt{1.4 = 1.02^n}}$

$\implies{\tt{1.02^1^7 = 1.02^n}}$

$\implies\large{\boxed{\text{n = 17}}}$

Therefore, after 17 years the total increase in the population will be 40% of that of initial population.

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Answer 2

Question :-

the population of a village is 5000 and it increases at yeh rate 2% every year. after 2 years the population will be..?

Answer :-

→ After two years population is 5202

→ increasing in population after 2 years is 102 .

Formula used :-

$\implies \: P { \bigg(1 + \frac{R}{100} \bigg) }^{T}$

Step - by - step explanation :-

Given that :-

Assume that,

• P = 5000

• R = 2%

• Time = T

Solution :-

Substitute the given value in the given formula ,

• Population increase every year ( taken time T = 1)

$\implies \: 5000 { \bigg(1 + \frac{2}{100} \bigg) }^{1} \\ \\ \implies \: 5000 \times \frac{51}{50} \\ \\ \implies \: 5100$

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• After 2 years ( taken time T = 2)

$\implies \: 5000 { \bigg(1 + \frac{2}{100} \bigg) }^{2} \\ \\ \implies \: 5000 \times \frac{51}{50} \: \times \frac{51}{50} \\ \\ \implies \: 5202$

Increase in population after 2 years is ↓

→ 5202 - 5100

→ 102

Therefore ,

Population after 2 years is 5202.

Increase in population after 2 years is 102 .

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