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Question

The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.
(i) Find the population in 2001.
(ii) What would be its population in 2005?

Solution
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Given:

The population of a place increased to 54,000 in 2003

i)

To find population in 2001

Here,

New population A=54,000
Time from 2001 to 2003 is (n)=2 yrs
R=5%
Original population P=?

A=P(1+R100)2

54000=P(1+5100)2

54000=P(105100)2

54000×(100105)2=P

54000×100×100105×105=P

48979.59=P

Since the population is always a whole number.

So, P=48980 [Since, rounded to tens.]

Therefore, Population in 2001 was 48,980.

ii)

To find population in 2005.

Here, P=54000

R=5%

Population in 2005 is A=?

From 2003 to 2005, time (n)=2

A=P(1+R100)2

A=54000(1+5100)2

A=54000(105100)2

A=54000×105×105100×100

A=5.4×105×105

A=59535

Therefore, Population in 2005 will be 59,535.

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