Quandaries & Queries - Math Central

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shahrukh, a student:

Demographics
Each year for 10 years ,the population of a city increased by 5% of its value in the previous year.
If the initial population was 200 000 ,what was the population after 10 years ??

Shahrukh,

The population at the beginning of the first year is 200 000 and it increases by 5% by the end of the year, thus the population at the end of the first year is
200 000 + 0.05 x 200 000 = 200 000 x (1.05)
Hence the population at the beginning of the second year is 200 000 x (1.05) and it increases by 5% by the end of the year, thus the population at the end of the second year is
[200 000 x (1.05)] + 0.05 x [200 000 x (1.05)] = [200 000 x (1.05)] x (1.05) = 200 000 x (1.05)2
What is the population at the end of the third year?
What is the population at the end of the tenth year?

Penny

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