Question

the population of a city was 20,000 in the year 1997 . it was increases at the rate of 5% p. a find the population at the end of the Year 2000 ?​

Answer 1

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the population of a city was 20,000 in the year 1997 . it was increases at the rate of 5% p. a find the population at the end of the Year 2000 ?

$\huge\bold{ Solutions:-}$

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there is 5% increase in population every year,so every new year.thus, we can say it is increasing in compound Form.

population in the beginning 1998 =20,000 ( we treat this is the principal for the 1st year )

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Increase at 5% = 5/100× 20000=1000

population in 1999

20000+ 1000=21000(treat as the principal for second year)

increase at 5% =5/100×21000 =1050

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populations in 2000

21000+1050=22050( treat as the principal for the 3rd year)

increase at 5% =5/100×22050

= 1102.5

at the end of 2000 population= 22050+1102.5

= 23152.5

or,

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population at the end of 2000=20000(1+5/100 )

$2000 \times \frac{21}{20} \times \frac{21}{20} \times \frac{21}{20} \\ = 23153.$

so estimated population =23153.

#answerwithquality #bal

Answer 2

ＡＮＳＷＥＲ:

ᴛʜᴇʀᴇ ɪs 5% ɪɴᴄʀᴇᴀsᴇ ɪɴ ᴘᴏᴘᴜʟᴀᴛɪᴏɴ ᴇᴠᴇʀʏ ʏᴇᴀʀ,sᴏ ᴇᴠᴇʀʏ ɴᴇᴡ ʏᴇᴀʀ.ᴛʜᴜs, ᴡᴇ ᴄᴀɴ sᴀʏ ɪᴛ ɪs ɪɴᴄʀᴇᴀsɪɴɢ ɪɴ ᴄᴏᴍᴘᴏᴜɴᴅ ғᴏʀᴍ.

ᴘᴏᴘᴜʟᴀᴛɪᴏɴ ɪɴ ᴛʜᴇ ʙᴇɢɪɴɴɪɴɢ 1998 =20,000 ( ᴡᴇ ᴛʀᴇᴀᴛ ᴛʜɪs ɪs ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ғᴏʀ ᴛʜᴇ 1sᴛ ʏᴇᴀʀ )

ɪɴᴄʀᴇᴀsᴇ ᴀᴛ 5% = 5/100× 20000=1000

ᴘᴏᴘᴜʟᴀᴛɪᴏɴ ɪɴ 1999

20000+ 1000=21000(ᴛʀᴇᴀᴛ ᴀs ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ғᴏʀ sᴇᴄᴏɴᴅ ʏᴇᴀʀ)

ɪɴᴄʀᴇᴀsᴇ ᴀᴛ 5% =5/100×21000 =1050

ᴘᴏᴘᴜʟᴀᴛɪᴏɴs ɪɴ 2000

21000+1050=22050( ᴛʀᴇᴀᴛ ᴀs ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ғᴏʀ ᴛʜᴇ 3ʀᴅ ʏᴇᴀʀ)

ɪɴᴄʀᴇᴀsᴇ ᴀᴛ 5% =5/100×22050

= 1102.5

ᴀᴛ ᴛʜᴇ ᴇɴᴅ ᴏғ 2000 ᴘᴏᴘᴜʟᴀᴛɪᴏɴ= 22050+1102.5

= 23152.5

ᴏʀ,

ᴘᴏᴘᴜʟᴀᴛɪᴏɴ ᴀᴛ ᴛʜᴇ ᴇɴᴅ ᴏғ 2000=20000(1+5/100 )

\ʙᴇɢɪɴ{ʟɢᴀᴛʜᴇʀᴇᴅ}2000 \ᴛɪᴍᴇs \ғʀᴀᴄ{21}{20} \ᴛɪᴍᴇs \ғʀᴀᴄ{21}{20} \ᴛɪᴍᴇs \ғʀᴀᴄ{21}{20} \\ = 23153. \\\ᴇɴᴅ{ʟɢᴀᴛʜᴇʀᴇᴅ}2000×2021×2021×2021=23153.

$thanks$