Problem

A town has a population of 19000 and grows at $4.5 \%$ every year. To the nearest year, how long will it be until the population will reach 51600 ?

Answer

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Answer

Round the result to the nearest year: \(\boxed{23}\) years

Steps

Step 1 ：Use the exponential growth formula: \(Years = \frac{\log(\frac{FinalPopulation}{InitialPopulation})}{\log(1 + GrowthRate)}\)

Step 2 ：Plug in the given values: \(Years = \frac{\log(\frac{51600}{19000})}{\log(1 + 0.045)}\)

Step 3 ：Calculate the result: \(Years \approx 22.6977\)

Step 4 ：Round the result to the nearest year: \(\boxed{23}\) years

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