Question

the population of Hyderabad was 6809000 in a year 2011 if it increases at the rate of 4.7% per annum. what will be the population at the end of the year 2015
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Answer 1

Answer:

Given :-

The population of Hyderabad was 6809000 in a year 2011.

It increases at the rate of 4.7% per annum.

To Find :-

What is the population at the end of the year 2015.

Formula Used :-

$\bigstar \: \: \sf\boxed{\bold{\pink{A =\: P\bigg(1 + \dfrac{r}{100}\bigg)^n}}}\: \: \: \bigstar$

where,

A = Present Population

P = Initial Population

r = Rate of Interest

n = Number of Years

Solution :-

First, we have to find the number of years :

$\implies \sf Number\: of\: years (n) =\: 2015 - 2011$

$\implies \sf\bold{\purple{Number\: of\: years (n) =\: 4\: years}}$

Now, we have to find the present population at the end of the year 2015 :

Given :

Initial Population = 6809000

Rate of Interest = 4.7% per annum

Number of years = 4 years

According to the question by using the formula we get,

$\implies \sf A =\: 6809000\bigg(1 + \dfrac{4.7}{100}\bigg)^4$

$\implies \sf A =\: 6809000\bigg(\dfrac{100 + 4.7}{100}\bigg)^4$

$\implies \sf A =\: 6809000\bigg(\dfrac{104.7}{100}\bigg)^4$

$\implies \sf A =\: 6809000\bigg(\dfrac{104.7}{100} \times \dfrac{104.7}{100} \times \dfrac{104.7}{100} \times \dfrac{104.7}{100}\bigg)$

$\implies \sf A =\: 6809000\bigg(\dfrac{104.7 \times 104.7 \times 104.7 \times 104.7}{100 \times 100 \times 100 \times 100}\bigg)$

$\implies \sf A =\: 6809000\bigg(\dfrac{120167417.1681}{100000000}\bigg)$

$\implies \sf A =\: 6809000(1.20167417168)$

$\implies \sf A =\: 6809000 \times 1.20167417168$

$\implies \sf\bold{\red{A =\: 8182199}}$

$\therefore$ The present population at the end of the year 2015 is 8182199 .

Answer 2

Answer:

The population of Hyderabad was 6809000 in the year 2011.

It increases by 4.7% per annum.

we need to calculate population after 4 years with given rate of interest.

We will use the compounding formula

Z=A+(1+rupon100)t

where Z is population at the end  of duration

A is present population

t is time perior  

r is rate of interest

we know that 4.7% =0.047

putting the values

Z=6809000+(1+4.7upon100)4

Z=6809000(1.047)4

Z=6809000×1.2016741717

Z=8182199

Thus population at the end of 2015 will be 8182199..

 

Step-by-step explanation: