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If a town with a population of \(500\) doubles in size every \(9\) years, what will the population be \(36\) years from now?

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Full solution

Q. If a town with a population of \(500\) doubles in size every \(9\) years, what will the population be \(36\) years from now?
  1. Initial Population: Initial population: 500500 Doubling period: 99 years Total time: 3636 years
  2. Calculate Doubling Periods: Calculate the number of doubling periods in 3636 years. Number of periods = 369=4\frac{36}{9} = 4
  3. Population Growth Formula: Use the formula for population growth: P=P0imes2nP = P_0 imes 2^n P0=500P_0 = 500, n=4n = 4 P=500imes24P = 500 imes 2^4
  4. Calculate Exponential Value: Calculate 242^4. 24=162^4 = 16
  5. Final Population Calculation: Multiply the initial population by 1616. P=500imes16=8000P = 500 imes 16 = 8000

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