Question

The Population of a place increased to 54000 in 2003 at the rate of 5% per annum. Find the population in 2001 and in 2005 ?​

Answer 1

we use formula of amount of compound interest to find population 

A( 2003)= 54,000,

R =

5%, 

n = 2

years

 

In 2001 Population would be less than 2003 in two years.

A(2003)= P(2001)(1+R/100)^n

54000 = P (2001)(1+5/100)²

54000 = P(2001)(1+1/20)²

54000= P(2001)(21/20)²

54000 = P(2001)((21×21)/(20×20))

P(2001)=( 54000×20×20)/21×21

Population in 2001 = 48979.59= 48980(approx)

(ii) ATQ, population is increasing. Therefore population in 2005,

 

A(2005)= P(1+R/100)^n

= 54000(1+5/100)²

= 54000(1+1/20)²

= 54000( 21/20)²

= 54000(21/20)× (21/20)

=( 54000× 441)/ 400

=( 540×441)/4

= 238140/4

= 59535

Population in 2005= 59535

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Hope this will help you....

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Answer 2

Answer :  

Population in 2001 is 48980 approximately.

Population in 2005 is 59535.

Step-by-step explanation :

Given, Population of place in 2003 = 54000

It has got a increase of 5% per annum.

So, 5% is compounded rate.

Using the formula,

$A=P(1+\frac{R}{100})^n$

Here,

A = population in year 2003 = 54000

P = population in year 2001

R = 5%

n = number of years = 2003 - 2001 = 2

Substituting the values in formula,

⇒$54000=P(1+\frac{5}{100})^2$

⇒$A=P(1+\frac{1}{20})^2$

⇒$54000=P(\frac{20+1}{20})^2$

⇒$54000=P(\frac{21}{20})^2$

⇒$54000=P\times (\frac{441}{400})$

⇒$\frac{54000\times 400}{441}=P$

⇒$P=\frac{54\times 4\times 100000}{441}$

⇒$P=\frac{21600000}{441}$

⇒$P=48979.59$

Population in 2001 is 48980 approximately.

Now,

Given, Population of place in 2003 = 54000

It has got a increase of 5% per annum.

So, 5% is compounded rate.

Using the formula,

$A=P(1+\frac{R}{100})^n$

Here,

A = population in year 2003 = 54000

P = population in year 2001

R = 5%

n = number of years = 2005 - 2003 = 2

Substituting the values in formula,

⇒$54000=P(1+\frac{5}{100})^2$

⇒$A=P(1+\frac{1}{20})^2$

⇒$54000=P(\frac{20+1}{20})^2$

⇒$54000=P(\frac{21}{20})^2$

⇒$P=54000\times (\frac{21\times 21}{20\times 20})$

⇒$P=54000\times (\frac{441}{400})$

⇒$P=\frac{540}{4}\times 441$

⇒$P=\frac{270}{2}\times 441$

⇒$P=135\times 441$

⇒$P=59535$

Population in 2005 is 59535.