Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

How come??

The population of a city in the year 2000 is 225,000. If the population decreases by 1.5% every year, what will be the population in 2004?

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: How come??

I'll assume population decrease is compounded, the formula for which is as a follows:

Here we have

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Re: How come??

hey I got it thanks a lot

kmadhyan

Member

Registered: 2007-08-30

Posts: 4

Re: How come??

Lets do it step by step instead of using formula...

Since
In 2001 it would be

A2001=A2000-A2000*r/100
Hence A2001=A2000(1-r/100)

Similiarly A2002=A2001(1-r/100)

A2003=A2002(1-r/100)
A2004=A2003(1-r/100)=A2002(1-r/100)^2=A2001(1-r/100)^3=A2000(1-r/100)^4

Hence A2004=A2000(1-r/100)^4

This is from where actual formula arises..............
Benefit of doing step by step is like if rate changes every year.........r1,r2,r3,r4

Formula would be

A2004=A2000(1-r1/100)(1-r2/100)(1-r3/100)(1-r4/100)

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IT is maths which has brought humanity from Ice Age to Present