Statement 1: The population of a town in the year 2024 is x and it increases by 10% every year. The population of in the year 2021 was = x Statement 2: If the population increases from year 2021 to year 2024 at the rate of 10%, then corresponding decrease from 2024 to 2021 is 10 x 3%. 1. Both the statements are true. 2. Both the statements are false. 3. Statement 1 is true, and statement 2 is false. 4. Statement 1 is false, and statement 2 is true.

Question

KnowledgeBoat · Accepted Answer

The general formula for population growth with a fixed annual percentage increase is: Pt = Po where, Pt = Population after t years P0 = Initial population r = Annual growth rate (in percentage) t = Time in years Given, the population in 2024 is x, and the annual growth rate is 10%. To find the population in 2021, we need to go back 3 years (from 2024 to 2021). Rearranging the formula to solve for P0 = ⇒ P0 = So, statement 1 is false. If the population increases from year 2021 to year 2024 at the rate of 10%. Let P0 be the population in 2021 and Pt be the population in 2024. ⇒ Pt = P0 ⇒ Pt = P0 (1 + 0.1)3 ⇒ Pt = P0 x 1.13 ⇒ Pt = 1.331P0 The percentage decrease = So, statement 2 is false. ∴ Both the statements are false. Hence, option 2 is correct option.

Mathematics

Compound Interest

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