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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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Example 9 The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.Population of city in 1997 = 20,000 It Increases at the Rate of 5% Per Annum Here, 5% is compounded Rate So we use the formula A = P (𝟏+𝑹/𝟏𝟎𝟎)^𝒏 Here, A = Population at end of 2000 P = Population in 1997 = 20,000 R = 5 % N = 2000 − 1997 = 3 Putting Values in Formula Population at end of 2000 = 20000 (𝟏+𝟓/𝟏𝟎𝟎)^𝟑 = 20000 (1+1/20)^3 = 20000 ((20 + 1)/20)^3 = 20000 (𝟐𝟏/𝟐𝟎)^𝟑 = 20000 × (21 × 21 × 21)/(20 × 20 × 20) = (5 × 21 × 21 × 21)/2 = (441 × 21 × 5)/2 = (441 × 105)/2 = 46305/2 = 23152.5 Since population cannot be in decimals ∴ Estimated Population = 23,153

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.